F1421 Basic mathematical methods in physics 1

Faculty of Science
Autumn 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
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. 281 pp. Vysokoškolské učebnice. ISBN 80-214-2914-3. 2006. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia. 383 s. ISBN 8020000887. 1997. 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). 697 pp. ISBN 978-80-214-4071-5. 2012. 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.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (Autumn 2024, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2024/F1421