MU:MU01104 Mathematical Analysis IV

MU01104 Mathematical Analysis IV

Mathematical Institute in Opava
Summer 2019

Extent and Intensity

3/0/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

Vladimír Averbuch, DrSc. (lecturer)

Guaranteed by

Vladimír Averbuch, DrSc.
Mathematical Institute in Opava

Prerequisites (in Czech)

MU01904 Mathematical Analysis IV - Exe

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

Syllabus

1. Riemann integral (divisions, null sets, oscillation, Lebesgue theorem, Fubini's theorem, partition of unity, change of variable in the integral).
2. Differential forms (tensors, anti-symmetric tensors, differential forms, exterior differentiation).
3. Stokes theorem (chains, integral over a chain, Stokes theorem for chains, manifolds, tangent space, orientation, Stokes theorem for manifolds, theorems on rotation and divergence).
4. Basics of complex analysis (functions of one complex variable, derivatives and integrals in the complex domain, Cauchy's residue theorem and its consequences).
5. Ordinary differential equations (theorem on existence and uniqueness, solution methods, linear equations).

Literature

recommended literature

V. I. Averbuch, M. Málek. Matematická analýza III, IV. MÚ SU, Opava, 2003. URL info
D. Krupka. Úvod do analýzy na varietách. SPN, Praha, 1986. info
M. Spivak. Matematičeskij analiz na mnogoobrazijach. Mir, Moskva, 1968. info
V. Jarník. Integrální počet I. ČSAV, Praha, 1963. info
V. Jarník. Integrální počet II. ČSAV, Praha, 1963. info

Language of instruction

English

Further Comments

The course can also be completed outside the examination period.