F1421 Basic mathematical methods in physics 1

Faculty of Science
Autumn 2018
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 17. 9. to Fri 14. 12. Mon 8:00–10:50 F1 6/1014
Prerequisites
Secondary school mathematics. Basic operations of differential and integral calculus on the secondary school level are appropriate (but not necessary).
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. Derivatives and integrals of one variable real function, basic operations.
  • 2. Derivatives and integrals: applications in mechanics.
  • 3. 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,transformation rules.
  • 4. Ordinary differential equations: first order ODE: separation of variables, first-order linear differential equations, physical applications (nuclear fission, absorption of radiation), second order ODE.
  • 5. Second order ODE and simple systems od ODE: applications in physics: equations of a particle motion, harmonic oscillator, charged particles in fields, damped and forces oscillations.
  • 6. Coordinate systems.
  • 7. Path integrals: 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 of a force along the curve).
  • 9. Scalar function of two and three variables: derivatives in the given direction, partial derivatives, 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 - Maxwell distribution of speeds.
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
  • 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
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
Study Materials
The course is taught annually.
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 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2018, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2018/F1421