F1421 Basic mathematical methods in physics 1

Faculty of Science
Autumn 2008
Extent and Intensity
2/1. 4 credit(s) (plus extra credits for completion). Type of Completion: graded credit.
Teacher(s)
Mgr. Lenka Czudková, Ph.D. (lecturer)
Mgr. Marek Chrastina, Ph.D. (seminar tutor)
Mgr. Martin Bureš, 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.
Timetable
Thu 10:00–11:50 F4,03017
  • Timetable of Seminar Groups:
F1421/01: Thu 7:00–7:50 F4,03017, M. Chrastina
F1421/02: Wed 17:00–17:50 F2 6/2012, M. Bureš
Prerequisites
It is recommended to master basic operations of differential and integral calculus on the secondary school level.
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 one variable and many variables function, ordinary differential equations) and algebra (vector algebra in twodimensional and threedimensional 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; get routine numerical skills necessary for 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. Double integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a surface).
  • 12. Triple integral, methods of calculation (Fubini theorem, transformation of coordinates), physical and geometric applications (mass, centre of mass, moment of inertia of a body).
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
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
Assessment methods
graded credit (3 written tests during the semester, homeworks, necessity to frequent the course (this requirement is possible to compensate by solving examples))
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
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 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, Autumn 2024.
  • Enrolment Statistics (Autumn 2008, recent)
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