PřF:F1421 Basic mathematical methods in - Course Information
F1421 Basic mathematical methods in physics 1
Faculty of ScienceAutumn 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 10:00–12:50 F1 6/1014
- Prerequisites
- It is recommended to master basic operations of differential and integral calculus on the secondary school level.
- Course Enrolment Limitations
- The course is offered to students of any study field.
- 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 one variable and many variables function, ordinary differential equations) and algebra (vector algebra in two-dimensional and three-dimensional spaces). 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 trained in the seminar F1422.
- Learning outcomes
- At the end of the course student will be able to apply basic concepts of the mathematical analysis, algebra and theory of the probability (see Course Contents) to the situations typical for the bachelor course of general physics.
- Syllabus
- 1. Derivation and integral of one variable real function, practising of basic operations.
- 2. Fundamentals of vector algebra in R-2 and R-3: vectors, vector calculus, scalar and vector product and their geometrical and physical interpretation, calculus in bases.
- 3. Fundamentals of vector algebra in R-2 a R-3: transformation rules.
- 4. Ordinary differential equations: separation of variables, first-order linear differential equations, physical applications (nuclear fission, absorption of radiation).
- 5. Ordinary differential equations: linear equations of the second and higher order with the constant coefficients, physical applications (equations of a particle motion, harmonic oscillator, damped and forces oscillations).
- 6. Some simple systems of equations of motion.
- 7. Curvilinear coordinates.
- 8. Curvilinear integral: curves, parametrisation, integral of the first type and its physical application (length, mass, centre of mass and moment of inertia of the curve), integral of the second type and its physical application (work along the curve).
- 9. Scalar function of two and three variables: derivation in the given direction, partial derivations, gradient.
- 10. Scalar function of two and three variables: total differential, existence of potential.
- 11. Vector functions of two and three variables: definitions, Jacobi matrix, integral curves of the vector field (streamlines, field lines, ... ), differential operators.
- 12. Combinatorics and fundamentals of statistical distribution. Random variables: the probability, discrete and continuous distributions, characteristics of the distribution (mean, standard deviation, median, ... ), distribution function.
- 13. Random variables - applications: fundamentals of measurement results processing, physical problems.
- Literature
- required literature
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis). Brno: VUTIUM, 2006, 281 pp. Vysokoškolské učebnice. ISBN 80-214-2914-3. 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 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
- 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
- Follow-Up Courses
- Further Comments
- The course is taught annually.
- Enrolment Statistics (recent)
- Permalink: https://is.muni.cz/course/sci/autumn2024/F1421