F2712 Mathematics 2

Faculty of Science
Spring 2025
Extent and Intensity
4/3/0. 6 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Mgr. Pavla Musilová, Ph.D. (lecturer)
Guaranteed by
Mgr. Pavla Musilová, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Prerequisites
Grammar school mathematics, matter of Mathematics 1
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 discipline is a second part of Mathematics for students of bachelor studies of applied physics and non-physical programs. Its aim is to give students a knowledge and understanding of fundamental concepts of basic mathematical disciplines required for natural sciences and technical disciplines -- mathematical analysis, linear algebra and geometry, probability theory.
Learning outcomes
Absolving the discipline a student obtain following knowledge and skills:
understanding of the concept of linearity, ability of practical calculus in linear algebra and geometry (calculations with vectors and linear mappings in bases using matrix algebra solving eigenvalue problem)
skills in calculations using curvilinear coordinates
solving simple differential equations and systems of differential equations, and their use for applications in physics, geometry, technical disciplines, chemistry, etc
understanding of differential and integral calculus of n-variable functions
understanding of basic concepts of vector analysis and practical calculations including applications
Syllabus
  • 1. Linear mapping of vector spaces, eigenvalue problem.
  • 2. Basic of metric and topology spaces.
  • 3. Ordinary differential equations of first order.
  • 4. Ordinary differential equations of higer order.
  • 5. Systems of ordinary differential equations.
  • 6. Differential calculus of functions of n-variables.
  • 7. Applications of differential calculus of functions of n-variables.
  • 8. Mappings Euclidean spaces.
  • 9. Coordinate systems.
  • 10. Integral calculus of functions of n-variables - volume.
  • 11. Integral calculus of functions of n-variables - curve integrals.
  • 12. Integral calculus of functions of n-variables - surface integrals.
  • 13. Differential oparators in physics.
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
    not specified
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi III (Mathematics for understanding and praxis III). 1st ed. Brno: VUTIUM, VUT Brno, 2018, 1068 pp. ISBN 978-80-214-5503-0. info
Teaching methods
Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests
Assessment methods
Teaching: lectures and exercises
Exam: written test (solving problems and test), oral exam
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 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, 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.
  • Enrolment Statistics (recent)
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