F2422 Fundamental mathematical methods in physics 2

Faculty of Science
Spring 2023
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 12:00–14:50 F2 6/2012
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
The course gives the basic review of fundamental mathematical procedures used in physical theories, mainly those of mathematical analysis (differential and integral calculus of the many variables functions, vector analysis, surface integrals, integral theorems) and algebra (basic tensor calculus). 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 obtained in seminar F2423.
Learning outcomes
At the end of the course student will be able to apply advanced concepts of the mathematical analysis and algebra (see Course Contents) to the situations typical for the bachelor course of general physics.
Syllabus
  • 1. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 2. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
  • 3. Surfaces in threedimensional euclidean space: parametrizations, cartesian equations.
  • 4. Surface integral of the first type, physical characteristics of bodies (mass, center of mass, tensor of inertia).
  • 5. Surface integral of the second type, physical applications (flow of a vector field).
  • 6. Calculus of surface integrals.
  • 7. Integral theorems.
  • 8. Physical applications of integrals and integral theorems: Integral and differential form of Maxwell equations.
  • 9. Applications of integral theorems in fluid mechanics.
  • 10. Series of functions: Taylor series, physical applications (estimations).
  • 11. Series of functions: Fourier series, applications (Fourier analysis of a signal).
  • 12. Elements of tensor algebra.
Literature
    required literature
  • 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
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Assessment methods
Written examination, or successive oral examination. Student demonstrates his knowledge and practical skills of the topics of this course, and the ability do apply them to the concrete mathematics and physical situations.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, 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 2024, Spring 2025.
  • Enrolment Statistics (Spring 2023, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2023/F2422