F3423 Basic mathematical methods in physics 3

Faculty of Science
Autumn 2024
Extent and Intensity
2/2/0. 4 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Ing. arch. Petr Kurfürst, Ph.D. (lecturer)
Mgr. Ing. arch. Petr Kurfürst, Ph.D. (seminar tutor)
prof. RNDr. Jana Musilová, CSc. (seminar tutor)
Bc. Peter Burda (assistant)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Ing. arch. Petr Kurfürst, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Tue 10:00–11:50 F1 6/1014
  • Timetable of Seminar Groups:
F3423/01: Tue 8:00–9:50 Fs1 6/1017
Prerequisites
It is recommended to previously pass the courses F1421 Basic mathematical methods in physics 1 and F2422 Basic mathematical methods in physics 2, or F1422 Computing Practice 1 and F2423 Computing Practice 2
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Acquisition of more advanced mathematical skills, usable at the end of the bachelor's study, in master's studies, and in subsequent physical practice.
Learning outcomes
After passing the course, the student will be able to use more complex analytical and numerical mathematical methods (see the Course Contents) in more advanced areas of physics, especially in quantum mechanics, plasma physics, theory of relativity, field theory, etc.
Syllabus
  • 1. Linear algebra - linear operators in vector spaces, eigenvectors and eigenvalues, linear operators in scalar product spaces, physical applications. (JM) 2. Ordinary differential equations (repetition), systems of linear differential equations. Application: Chains of atoms with different boundary conditions. Differential equation of the 2nd order with non-constant coefficients. (PK) 3. Functions of a complex variable (repetition). Laplace transform, convolution, physical applications, numerical calculations. (JM, PK numerical calculations) 4. Fourier transformation, convolution, physical applications, numerical calculations. (JM, PK numerical calculations) 5. Tensor algebra, covariant and contravariant tensors, tensor fields. (JM) 6. Physical applications of tensor algebra and analysis. (JM) 7. Curvilinear coordinates (cylindrical, spherical, general), areas, volumes, position, velocity and acceleration in curvilinear coordinates. (PK) 8. Partial differential equations of the first and second order. Classification of equations, examples of analytical solutions. (PK) 9. Numerical methods of linear algebra, theoretical basis and programming of physical problems (Matlab, Phyton, Fortran). (JM theory, PK calculations) 10. Numerical interpolation and regression, theoretical basis and programming. (JM theory, PK calculations) 11. Numerical derivation and integration of functions of one variable, solution of ordinary differential equations. (JM theory, PK calculations) 12. Numerical methods of calculating functions of several variables - solving partial differential equations. (PK) 13. Reserve
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
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • ARFKEN, George B. and Hans-Jurgen WEBER. Mathematical methods for physicists. 6th ed. Amsterdam: Elsevier, 2005, xii, 1182. ISBN 0120598760. info
  • KURFÜRST, Petr. Praktické početní metody pro fyziky (Practical computing methods for physicists). 1. vyd. Brno: Masarykova univerzita, 2023. Elportál. ISBN 978-80-280-0430-9. PURL html url info
  • KURFÜRST, Petr. Početní praktikum (Computing practice). 2. vyd. Brno: Masarykova univerzita, 2017, 155 pp. Elportál. ISBN 978-80-210-8686-9. URL URL URL info
Teaching methods
Lecture: theoretical course with examples. Exercises: practical application of lectured mathematical methods, development of more complex problems in the form of homeworks.
Assessment methods
Solving more complex homeworks and subsequent oral exam. During an individual discussion, the student demonstrates theoretical knowledge from individual subjects as well as the ability to apply them to practical mathematical and physical situations.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
http://www.physics.muni.cz/~petrk/
Precondition for access to the exam: 75% participation in the exercises, completion of assigned tasks according to the teacher's instructions.
The course is also listed under the following terms Autumn 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2024/F3423