## MU02036 Mathematical Methods in Physics and Engineering II

Mathematical Institute in Opava
Summer 2021
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Oldřich Stolín, Ph.D. (lecturer)
RNDr. Oldřich Stolín, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Oldřich Stolín, Ph.D.
Mathematical Institute in Opava
Timetable
Mon 10:35–12:10 110
• Timetable of Seminar Groups:
MU02036/01: Wed 14:45–16:20 110, O. Stolín
Prerequisites (in Czech)
( MU02034 Methods in Physics and Enginee || MU02035 Math. Methods in Physic Eng. I ) && TYP_STUDIA ( BN )
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)
Student dokáže teoreticky popsat a prakticky používat základní matematické metody řešení fyzikálních a technických úloh.
Syllabus
• 1. variational calculus; variational functionals, lagrangian mechanics, Lagrange multipliers.
2. Function spaces; norms, inner products, operators, distributions.
3. Linear ordinary differential equations; existence and uniqueness of solutions, normal form, non-homegeneity, singularity.
4. Linear differential operators; formal operator and its extensions, adjoint operator, completeness of eigenfunctions.
5.Green's functions; nonhomogeneous linear differential equations, construction of Green's functions, use of the Lagrange identity, eigen-function expansion, analytic properties, Gelfand-Dikii equation.
6. Linear partial differential equations; classification of second order equations, Cauchy conditions, wave equations, heat equation, Laplace equation.
7. The mathematics of waves, waves in dispersive media, creation of waves, nonlinear waves, solitons.
8. Special functions; curvilinear coordinate systems, spheric harmonics, Bessel functions, Weyl theorem.
9. Dynamical systems; autonomous and nonautonomous systems, their relationship and best known special cases.
10. One-dimensional digital filters; Nyiquist teorém, Heisenberg relations, linear and nonlinear examples.
11. Linear integral equations; classification, integral transforms, separable kernels, singular equations.
Literature
required literature
• Stone M. Mathematics for Physics I. Alexandria, Pimander-Casaubon, 2002. info
recommended literature
• Smékal Z., Vich R. Číslicové filtry. Praha, Academia, 2000. info
• Pierre N. V. Dynamical Systems. Berlin, Springer, 1994. info
• Dettman, J. W. Matematické metody ve fyzice a technice. Academia, Praha, 1970. info
not specified
• J. Segethová. Základy numerické matematiky. Karolinum, Praha, 1998. ISBN 80-7184-596-5. info
• E. Vitásek. Numerické metody. SNTL, Praha, 1987. info
• Z. Riečanová a kol. Numerické metody a matematická štatistika. Alfa, Bratislava, 1987. ISBN 063-559-87. info
• K. Rektorys a spolupracovníci. Přehled užité matematiky. SNTL, Praha, 1968. info
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020.
• Enrolment Statistics (recent)