F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2024
Extent and Intensity
3/0/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Mon 19. 2. to Sun 26. 5. Mon 8:00–10:50 F1 6/1014
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Learning outcomes
At the end of the course student will be able to apply advanced concepts of the mathematical analysis and algebra (see Course Contents) to the situations typical for the bachelor course of general physics.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimensional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the second type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Written examination, or successive oral examination. Student demonstrates his knowledge and practical skills of the topics of this course, and the ability do apply them to the concrete mathematics and physical situations.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2025
Extent and Intensity
3/0/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Learning outcomes
At the end of the course student will be able to apply advanced concepts of the mathematical analysis and algebra (see Course Contents) to the situations typical for the bachelor course of general physics.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimensional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the second type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Written examination, or successive oral examination. Student demonstrates his knowledge and practical skills of the topics of this course, and the ability do apply them to the concrete mathematics and physical situations.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2023
Extent and Intensity
3/0/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Mon 12:00–14:50 F2 6/2012
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Learning outcomes
At the end of the course student will be able to apply advanced concepts of the mathematical analysis and algebra (see Course Contents) to the situations typical for the bachelor course of general physics.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimensional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the second type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Written examination, or successive oral examination. Student demonstrates his knowledge and practical skills of the topics of this course, and the ability do apply them to the concrete mathematics and physical situations.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2022
Extent and Intensity
3/0/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Mon 12:00–14:50 F1 6/1014
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Learning outcomes
At the end of the course student will be able to apply advanced concepts of the mathematical analysis and algebra (see Course Contents) to the situations typical for the bachelor course of general physics.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimensional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the second type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Written examination, or successive oral examination. Student demonstrates his knowledge and practical skills of the topics of this course, and the ability do apply them to the concrete mathematics and physical situations.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2021
Extent and Intensity
3/0/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Mon 1. 3. to Fri 14. 5. Mon 12:00–14:50 F1 6/1014
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Learning outcomes
At the end of the course student will be able to apply advanced concepts of the mathematical analysis and algebra (see Course Contents) to the situations typical for the bachelor course of general physics.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimensional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the second type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Written examination, or successive oral examination. Student demonstrates his knowledge and practical skills of the topics of this course, and the ability do apply them to the concrete mathematics and physical situations.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2020
Extent and Intensity
3/0/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Mon 11:00–13:50 F3,03015
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Learning outcomes
At the end of the course student will be able to apply advanced concepts of the mathematical analysis and algebra (see Course Contents) to the situations typical for the bachelor course of general physics.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimensional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the second type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Written examination, or successive oral examination. Student demonstrates his knowledge and practical skills of the topics of this course, and the ability do apply them to the concrete mathematics and physical situations.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2019
Extent and Intensity
3/0/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Mon 18. 2. to Fri 17. 5. Mon 13:00–15:50 F4,03017
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimensional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the second type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Oral examination. During individual discussion student demonstrate his theoretical knowledge of the topics of this course, and the ability do apply them to the concrete practical mathematics and physical situations.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
spring 2018
Extent and Intensity
3/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Wed 16:00–18:50 F4,03017
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimensional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the second type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Oral examination. During individual discussion student demonstrate his theoretical knowledge of the topics of this course, and the ability do apply them to the concrete practical mathematics and physical situations.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2017
Extent and Intensity
3/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Mon 20. 2. to Mon 22. 5. Wed 17:00–19:50 F3,03015
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimensional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the second type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Oral examination. During individual discussion student demonstrate his theoretical knowledge of the topics of this course, and the ability do apply them to the concrete practical mathematics and physical situations.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2016
Extent and Intensity
3/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Thu 12:00–14:50 F1 6/1014
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimensional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the second type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Oral examination. During individual discussion student demonstrate his theoretical knowledge of the topics of this course, and the ability do apply them to the concrete practical mathematics and physical situations.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2015
Extent and Intensity
3/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Thu 15:00–17:50 F1 6/1014
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimensional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the second type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Oral examination. During individual discussion student demonstrate his theoretical knowledge of the topics of this course, and the ability do apply them to the concrete practical mathematics and physical situations.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2014
Extent and Intensity
3/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Mon 13:00–15:50 F3,03015
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimensional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the second type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Oral examination. During individual discussion student demonstrate his theoretical knowledge of the topics of this course, and the ability do apply them to the concrete practical mathematics and physical situations.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2013
Extent and Intensity
3/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Wed 8:00–10:50 F1 6/1014
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the secnond type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2012
Extent and Intensity
3/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Fri 7:00–9:50 F1 6/1014
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the secnond type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Written and oral examination.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2011
Extent and Intensity
3/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Timetable
Mon 7:00–9:50 F4,03017
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the secnond type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2010
Extent and Intensity
2/1. 4 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Mgr. Marek Chrastina, Ph.D. (seminar tutor)
Mgr. Martin Bureš, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Timetable
Mon 8:00–9:50 F1 6/1014
  • Timetable of Seminar Groups:
F2422/01: Tue 19:00–19:50 F4,03017, M. Chrastina
F2422/02: Wed 17:00–17:50 F3,03015, M. Chrastina
F2422/03: Wed 12:00–12:50 F3,03015, M. Bureš
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra; to get routine numerical skills necessary for bachelor course of general physics.
Syllabus
  • 1. Double and triple integral, methods of calculation, physical and geometric applications (revision).
  • 2. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations.
  • 3. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 4. Surface integral of the secnond type, physical applications (flow of a vector field).
  • 5. Calculus of surface integrals.
  • 6. Integral theorems.
  • 7. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 8. Applications of integral theorems in fluid mechanics.
  • 9. Series of functions: Taylor series, physical applications (estimations).
  • 10. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 11. Elements of tensor algebra.
Literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Teaching methods
Lectures: theoretical explanation with practical examples. Exercises: solving problems for understanding of basic concepts and theorems.
Assessment methods
graded credit (3 written tests during the semester, homeworks, necessity to frequent the course (this requirement is possible to compensate by solving examples))
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics

Faculty of Science
Spring 2009
Extent and Intensity
2/1. 4 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Mgr. Marek Chrastina, Ph.D. (seminar tutor)
Mgr. Martin Bureš, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Timetable
Wed 7:00–8:50 F2 6/2012
  • Timetable of Seminar Groups:
F2422/01: Thu 13:00–13:50 F2 6/2012, M. Chrastina
F2422/02: Wed 16:00–16:50 F1 6/1014, M. Bureš
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra; to get routine numerical skills necessary for bachelor course of general physics.
Syllabus
  • 1. Double and triple integral, methods of calculation, physical and geometric applications (revision).
  • 2. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations.
  • 3. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 4. Surface integral of the secnond type, physical applications (flow of a vector field).
  • 5. Calculus of surface integrals.
  • 6. Integral theorems.
  • 7. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 8. Applications of integral theorems in fluid mechanics.
  • 9. Series of functions: Taylor series, physical applications (estimations).
  • 10. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 11. Elements of tensor algebra.
Literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Assessment methods
graded credit (3 written tests during the semester, homeworks, necessity to frequent the course (this requirement is possible to compensate by solving examples))
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2008
Extent and Intensity
2/1. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Mgr. Marek Chrastina, Ph.D. (seminar tutor)
Mgr. Martin Bureš, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Timetable
Fri 12:00–13:50 F1 6/1014
  • Timetable of Seminar Groups:
F2422/01: Wed 16:00–16:50 F3,03015, M. Chrastina
F2422/02: Tue 12:00–12:50 F4,03017, M. Chrastina
F2422/03: Wed 13:00–13:50 F4,03017, M. Bureš
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Předmět je zaměřen na získání přehledu o základních matematických postupech používaných ve fyzikálních teoriích, především z oblasti matematické analýzy (diferenciální a integrální počet funkcí více proměnných, vektorová analýza, plošný integrál, integrální věty). Důraz je kladen na pochopení základních pojmů, výpočetní praxi a fyzikální aplikace.
Syllabus
  • 1. Double and triple integral, methods of calculation, physical and geometric applications (revision). 2. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations. 3. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia). 4. Surface integral of the secnond type, physical applications (flow of a vector field). 5. Calculus of surface integrals. 6. Integral theorems. 7. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations. 8. Applications of integral theorems in fluid mechanics. 9. Series of functions: Taylor series, physical applications (estimations). 10. Series of functions: Fourier series, applications (Fourier analysis of a signal). 11. Elements of tensor algebra.
Literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Assessment methods (in Czech)
přednáška+cvičení, klasifikovaný zápočet - viz podmínky v položce Informace učitele.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics

Faculty of Science
Spring 2007
Extent and Intensity
2/1. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Mgr. Marek Chrastina, Ph.D. (seminar tutor)
Mgr. Tomáš Nečas, Ph.D. (seminar tutor)
Mgr. Roman Šteigl, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Timetable
Wed 11:00–12:50 F2 6/2012
  • Timetable of Seminar Groups:
F2422/01: Thu 14:00–14:50 F4,03017, M. Chrastina
F2422/02: Thu 16:00–16:50 F4,03017, T. Nečas
F2422/03: Thu 12:00–12:50 F3,03015, R. Šteigl
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Předmět je zaměřen na získání přehledu o základních matematických postupech používaných ve fyzikálních teoriích, především z oblasti matematické analýzy (diferenciální a integrální počet funkcí více proměnných, vektorová analýza, plošný integrál, integrální věty). Důraz je kladen na pochopení základních pojmů, výpočetní praxi a fyzikální aplikace.
Syllabus
  • 1. Double and triple integral, methods of calculation, physical and geometric applications (revision). 2. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations. 3. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia). 4. Surface integral of the secnond type, physical applications (flow of a vector field). 5. Calculus of surface integrals. 6. Integral theorems. 7. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations. 8. Applications of integral theorems in fluid mechanics. 9. Series of functions: Taylor series, physical applications (estimations). 10. Series of functions: Fourier series, applications (Fourier analysis of a signal). 11. Elements of tensor algebra.
Literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Assessment methods (in Czech)
přednáška+cvičení, klasifikovaný zápočet - viz podmínky v položce Informace učitele.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics

Faculty of Science
Spring 2006
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (seminar tutor)
Mgr. Ondřej Přibyla (seminar tutor)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Tomáš Nečas, Ph.D. (seminar tutor)
Mgr. Roman Šteigl, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Timetable
Thu 15:00–16:50 F1 6/1014
  • Timetable of Seminar Groups:
F2422/01: Thu 17:00–17:50 F3,03015, L. Czudková
F2422/02: Mon 8:00–8:50 F2 6/2012, J. Musilová, T. Nečas
F2422/03: Mon 11:00–11:50 F1 6/1014, J. Musilová, O. Přibyla
F2422/04: Wed 18:00–18:50 F1 6/1014, J. Musilová, R. Šteigl
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Předmět je zaměřen na získání přehledu o základních matematických postupech používaných ve fyzikálních teoriích, především z oblasti matematické analýzy (diferenciální a integrální počet funkcí více proměnných, vektorová analýza, plošný integrál, integrální věty, diferenciální rovnice). Důraz je kladen na pochopení základních pojmů, výpočetní praxi a fyzikální aplikace.
Syllabus
  • 1. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations. 2. Quadratic surfaces, classification, physical applications. 3. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia). 4. Surface integral of the secnond type, physical applications (flow of a vector field). 5. Calculus of surface integrals. 6. Integral theorems. 7. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations. 8. Applications of integral theorems in fluid mechanics. 9. Series of functions: Taylor series, physical applications (estimations). 10. Series of functions: Fourier series, applications (Fourier analysis of a signal). 11. Integral transforms (fundamental properties), Laplace and Fourier transforms, applications (solving differential equations). 12. Some aspects of solving differential equations. 13. Reserved time.
Literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Assessment methods (in Czech)
přednáška+cvičení, klasifikovaný zápočet - viz podmínky v položce Informace učitele.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics

Faculty of Science
Spring 2005
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
Mgr. Pavla Musilová, Ph.D. (lecturer)
Mgr. Ondřej Přibyla (assistant)
Mgr. Petr Velan (seminar tutor)
doc. Mgr. Josef Klusoň, Ph.D., DSc. (seminar tutor)
Mgr. Martin Netolický (seminar tutor)
Mgr. Roman Šteigl, Ph.D. (seminar tutor)
Mgr. Martin Mráz (assistant)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Timetable
Wed 11:00–12:50 U-aula
  • Timetable of Seminar Groups:
F2422/01: Mon 8:00–9:50 F23-106, M. Netolický
F2422/02: Mon 17:00–18:50 F23-109, R. Šteigl
F2422/03: Tue 15:00–16:50 F23-106, J. Klusoň
F2422/04: Tue 10:00–11:50 F23-106, P. Velan
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Předmět je zaměřen na získání přehledu o základních matematických postupech používaných ve fyzikálních teoriích, především z oblasti matematické analýzy (diferenciální a integrální počet funkcí více proměnných, vektorová analýza, plošný integrál, integrální věty, diferenciální rovnice). Důraz je kladen na pochopení základních pojmů, výpočetní praxi a fyzikální aplikace.
Syllabus
  • 1. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations. 2. Quadratic surfaces, classification, physical applications. 3. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia). 4. Surface integral of the secnond type, physical applications (flow of a vector field). 5. Calculus of surface integrals. 6. Integral theorems. 7. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations. 8. Applications of integral theorems in fluid mechanics. 9. Series of functions: Taylor series, physical applications (estimations). 10. Series of functions: Fourier series, applications (Fourier analysis of a signal). 11. Integral transforms (fundamental properties), Laplace and Fourier transforms, applications (solving differential equations). 12. Some aspects of solving differential equations. 13. Reserved time.
Literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Assessment methods (in Czech)
přednáška+cvičení, klasifikovaný zápočet - viz podmínky v položce Informace učitele.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics

Faculty of Science
Spring 2004
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
Mgr. Ondřej Přibyla (seminar tutor)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Anna Campbellová, Ph.D. (seminar tutor)
doc. Mgr. Josef Klusoň, Ph.D., DSc. (seminar tutor)
Mgr. Aleš Paták, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc.
Timetable of Seminar Groups
F2422/01: No timetable has been entered into IS. A. Paták
F2422/02: No timetable has been entered into IS. J. Klusoň
F2422/03: No timetable has been entered into IS. O. Přibyla
F2422/04: No timetable has been entered into IS. A. Campbellová
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Předmět je zaměřen na získání přehledu o základních matematických postupech používaných ve fyzikálních teoriích, především z oblasti matematické analýzy (diferenciální a integrální počet funkcí více proměnných, vektorová analýza, plošný integrál, integrální věty, diferenciální rovnice). Důraz je kladen na pochopení základních pojmů, výpočetní praxi a fyzikální aplikace.
Syllabus
  • 1. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations. 2. Quadratic surfaces, classification, physical applications. 3. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia). 4. Surface integral of the secnond type, physical applications (flow of a vector field). 5. Calculus of surface integrals. 6. Integral theorems. 7. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations. 8. Applications of integral theorems in fluid mechanics. 9. Series of functions: Taylor series, physical applications (estimations). 10. Series of functions: Fourier series, applications (Fourier analysis of a signal). 11. Integral transforms (fundamental properties), Laplace and Fourier transforms, applications (solving differential equations). 12. Some aspects of solving differential equations. 13. Reserved time.
Literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Assessment methods (in Czech)
přednáška+cvičení, klasifikovaný zápočet - viz podmínky v položce Informace učitele.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics

Faculty of Science
Spring 2003
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
Mgr. Ondřej Přibyla (seminar tutor)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jana Musilová, CSc.
Timetable of Seminar Groups
F2422/01: No timetable has been entered into IS. P. Musilová, O. Přibyla
F2422/02: No timetable has been entered into IS. P. Musilová, O. Přibyla
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Předmět je zaměřen na získání přehledu o základních matematických postupech používaných ve fyzikálních teoriích, především z oblasti matematické analýzy (diferenciální a integrální počet funkcí více proměnných, vektorová analýza, křivkový a plošný integrál, integrální věty, diferenciální rovnice). Důraz je kladen na pochopení základních pojmů, výpočetní praxi a fyzikální aplikace.
Syllabus
  • 1. Basic operations with scalar and vector functions of many variables, derivative along a direction, gradient, divergence, rotation. 2. Double and triple integral, Fubini theorem, transformation of integrals. 3. Total differential of functions of many variables. 4. Curve integral of the first and second type, work of a force field. 5. Surface integral of the first and second type, flow of a vector field. 6. Integral theorems. 7. Physical applications of integrals. Integral and differential form of Maxwell equations. 8. Applications of integral theorems in fluid mechanics. 9. Fourier series, applications. 10.,11. Some aspects of solving differential equations.
Assessment methods (in Czech)
přednáška+cvičení, klasifikovaný zápočet - viz podmínky v položce Informace učitele.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Základní matematické metody ve Fyzice 2

Faculty of Science
Spring 2002
Extent and Intensity
2/1. 4 credit(s). Type of Completion: graded credit.
Teacher(s)
doc. Franz Hinterleitner, Ph.D. (lecturer)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Physics Section – Faculty of Science
Contact Person: doc. Franz Hinterleitner, Ph.D.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Základy vektorové analýzy: vektorové funkce v R^3, definice divergence, rotace, Laplaceova operátoru, pojem tenzoru, identity pro operátory vektorové analýzy; orientované integrační obory a jejich orientované okraje, integralní věty: Gaussova, Greeneova, Stokesova věta; jednoduché příklady Hamiltonových-Jacobiho diferenciálních rovnic, součtový ansatz k separaci proměnných; přehled o lineárních parciálních diferenciálních rovnic druheho řadu, součinový ansatz, příklady: jednorozměrné vedení tepla, jednorozměrná vlnová rovnice, Poissonova rovnice, Keplerův problém; metoda řešení diferenciálních rovnic pomoci Greenovy funkce.
Syllabus (in Czech)
  • Základy vektorové analýzy: vektorové funkce v R^3, definice divergence, rotace, Laplaceova operátoru, pojem tenzoru, identity pro operátory vektorové analýzy; orientované integrační obory a jejich orientované okraje, integralní věty: Gaussova, Greeneova, Stokesova věta; jednoduché příklady Hamiltonových-Jacobiho diferenciálních rovnic, součtový ansatz k separaci proměnných; přehled o lineárních parciálních diferenciálních rovnic druheho řadu, součinový ansatz, příklady: jednorozměrné vedení tepla, jednorozměrná vlnová rovnice, Poissonova rovnice, Keplerův problém; metoda řešení diferenciálních rovnic pomoci Greenovy funkce.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

Extent and Intensity
3/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the secnond type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Written and oral examination.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2011 - only for the accreditation
Extent and Intensity
3/0. 3 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). The understanding of fundamental concepts, calculus, and physical applications are emphasized. The main objectives can be summarized as follows: to get prompt review of basic terms of mathematical analysis and algebra. Routine numerical skills necessary for bachelor course of general physics are obtained in seminar F2423.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the secnond type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Written and oral examination.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

F2422 Fundamental mathematical methods in physics

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
2/1. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Mgr. Marek Chrastina, Ph.D. (seminar tutor)
Mgr. Roman Šteigl, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Předmět je zaměřen na získání přehledu o základních matematických postupech používaných ve fyzikálních teoriích, především z oblasti matematické analýzy (diferenciální a integrální počet funkcí více proměnných, vektorová analýza, plošný integrál, integrální věty). Důraz je kladen na pochopení základních pojmů, výpočetní praxi a fyzikální aplikace.
Syllabus
  • 1. Double and triple integral, methods of calculation, physical and geometric applications (revision). 2. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations. 3. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia). 4. Surface integral of the secnond type, physical applications (flow of a vector field). 5. Calculus of surface integrals. 6. Integral theorems. 7. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations. 8. Applications of integral theorems in fluid mechanics. 9. Series of functions: Taylor series, physical applications (estimations). 10. Series of functions: Fourier series, applications (Fourier analysis of a signal). 11. Elements of tensor algebra.
Literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Assessment methods (in Czech)
přednáška+cvičení, klasifikovaný zápočet - viz podmínky v položce Informace učitele.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (recent)