FC2702 Mathematics for Physicists

Faculty of Education
Autumn 2024
Extent and Intensity
2/0/4. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Petr Sládek, CSc. (lecturer)
Mgr. Ivana Medková, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Petr Sládek, CSc.
Department of Physics, Chemistry and Vocational Education – Faculty of Education
Contact Person: Jana Jachymiáková
Supplier department: Department of Physics, Chemistry and Vocational Education – Faculty of Education
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the subject is to acquire clear knowledge of the basics of higher mathematics. Emphasis is placed on the logical structure of this scientific discipline and on acquiring the knowledge and skills needed to master the physics course at university.
Learning outcomes
After completing the course, the Participant will acquire:
Knowledge: A comprehensive overview of knowledge on the topics Vectors, Differential and integral calculus of functions of one or more variables, differential equations, basics of vector analysis, orthogonal systems, Fourier series.
Skills: Be able to use basic definitions and sentences when solving simple and application problems. To understand the connection of the material being discussed with practical physical applications. Be able to perform a qualified estimation of values.
Attitudes: Acquire the values ​​of objectivity and the importance of scientific work.
Syllabus
  • Syllabus of lectures and exercises (by weeks or blocks):
  • I. Coordinates, vectors.
  • - 1. Cartesian coordinates on the line, v plane and space, polar coordinates.
  • - 2. Concept of vector, vector space, vector addition, scalar and vector product, concept of vector basis.
  • II. Functions of one variable
  • - 1. Graph of a function, basic properties of functions, some elementary functions, concept of limits and continuity.
  • - 2. Derivation of a function, investigation of the progress of a function by using derivatives, differential of a function.
  • - 3. Concept of primitive function, indefinite integral, calculation of indefinite integral, definite integral, its calculation, applications.
  • III. Sequences and series.
  • - 1. Sequences.
  • - 2. Numerical series, Taylor development.
  • IV. Functions of several variables.
  • - 1. Concept of multivariable function, basic properties of functions.
  • - 2. Partial derivatives
  • - 3. Fundamentals of integral calculus of functions of several variables.
  • - 4. Curve integrals of the first and second kind.
  • - 5. Graphs of functions of several variables.
  • - 6. Concept of limits in direction, existence and calculation of limits.
  • - 7. Second order partial derivative, total differential, Laplace operator.
  • - 8. Integral calculus of functions of several variables.
  • - 9. Area integrals of the first and second kind.
  • V. Fundamentals of differential equations.
  • - 1. Concept of differential equations, initial and boundary conditions, general solutions.
  • - 2. First order linear differential equations
  • VI. Differential equations.
  • - 1. First order linear differential equations.
  • - 2. Second order linear differential equations, selected partial differential equations.
  • VII. Fundamentals of vector analysis.
  • - 1. Rotation and divergence operators.
  • - 2. Flow of a vector field through a closed surface.
  • - 3. Potential vector field.
  • VIII. Orthogonal systems, Fourier series.
  • - 1. Basic concepts and definitions.
  • - 2. Examples of function development in Fourier series.
Literature
    required literature
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných. 1. vyd. Brno: Masarykova univerzita, 2009, vi, 272. ISBN 9788021049758. info
  • SLÁDEK, Petr and Václav VACEK. Matematika pro fyziky I a II. Elportál. Brno: Masarykova univerzita, 2009. ISSN 1802-128X. URL info
  • NOVÁK, Vítězslav. Diferenciální počet funkcí jedné reálné proměnné. 1. vyd. Brno: Masarykova univerzita v Brně, 2004, 158 s. ISBN 802103386X. info
  • NOVÁK, Vítězslav. Integrální počet v R. Vyd. 3., přeprac. Brno: Masarykova univerzita, 2001, 85 s. ISBN 8021027207. info
  • JIRÁSEK, František, Eduard KRIEGELSTEIN and Zdeněk TICHÝ. Sbírka řešených příkladů z matematiky. 2. nezměn. vyd. Praha: SNTL - Nakladatelství technické literatury, 1981, 817 s. URL info
    recommended literature
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Diferenciální počet funkcí více proměnných. 1. dotisk 3. vyd. Brno: Masarykova univerzita, 2010, 144 pp. ISBN 978-80-210-4159-2. info
  • HÁJEK, Jiří. Cvičení z matematické analýzy : diferenciální počet v R. 2. vyd. Brno: Masarykova univerzita, 2003, 103 s. ISBN 802103260X. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 2nd ed. Brno: Masarykova univerzita, 2001, 207 pp. ISBN 80-210-2589-1. info
  • HÁJEK, Jiří. Cvičení z matematické analýzy : diferenciální počet funkcí více proměnných. 2. vyd. Brno: Masarykova univerzita, 2000, 111 s. ISBN 8021024534. info
  • HÁJEK, Jiří. Cvičení z matematické analýzy : integrální počet v R. 1. vyd. Brno: Masarykova univerzita, 2000, 102 s. ISBN 8021022639. info
  • DULA, Jiří and Jiří HÁJEK. Cvičení z matematické analýzy : obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 1998, 74 s. ISBN 8021019751. info
  • DULA, Jiří and Jiří HÁJEK. Cvičení z matematické analýzy : nekonečné řady. 2. vyd. Brno: Vydavatelství Masarykovy univerzity, 1992, 76 s. ISBN 8021003855. info
  • NOVÁK, Vítězslav. Diferenciální počet funkcí více proměnných. Vyd. 1. Brno: Rektorát UJEP, 1983, 159 s. info
Teaching methods
lectures, exercises
Assessment methods
Colloquium, 3x written test, completing online worksheets
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Information on the extent and intensity of the course: 24 hodin.
Teacher's information
For students on a foreign placement (ERASMUS, etc.): Course requirements will be individually set in the context of the courses taken during the foreign placement and in accordance with the objectives and learning outcomes of the study programme.
  • Enrolment Statistics (recent)
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