F2422 Fundamental mathematical methods in physics

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
2/1. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: graded credit.
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Mgr. Marek Chrastina, Ph.D. (seminar tutor)
Mgr. Roman Šteigl, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Lenka Czudková, Ph.D.
Prerequisites
Differential and integral calculus of functions of one variable, theoretical background and practical calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Předmět je zaměřen na získání přehledu o základních matematických postupech používaných ve fyzikálních teoriích, především z oblasti matematické analýzy (diferenciální a integrální počet funkcí více proměnných, vektorová analýza, plošný integrál, integrální věty). Důraz je kladen na pochopení základních pojmů, výpočetní praxi a fyzikální aplikace.
Syllabus
  • 1. Double and triple integral, methods of calculation, physical and geometric applications (revision). 2. Surfaces in threedimansional euclidean space: parametrizations, cartesian equations. 3. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia). 4. Surface integral of the secnond type, physical applications (flow of a vector field). 5. Calculus of surface integrals. 6. Integral theorems. 7. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations. 8. Applications of integral theorems in fluid mechanics. 9. Series of functions: Taylor series, physical applications (estimations). 10. Series of functions: Fourier series, applications (Fourier analysis of a signal). 11. Elements of tensor algebra.
Literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Assessment methods (in Czech)
přednáška+cvičení, klasifikovaný zápočet - viz podmínky v položce Informace učitele.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.