MU:MU01004 Mathematical Analysis IV - Course Information
MU01004 Mathematical Analysis IV
Mathematical Institute in OpavaSummer 2016
- 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)
- ( MU20003 Mathematical Analysis III || MU01003 Mathematical Analysis III ) && 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
- Applied Mathematics (programme MU, B1101)
- Mathematical Analysis (programme MU, M1101)
- Mathematics (programme MU, B1101)
- Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz)
- Course objectives
- The main attention of the fourth part of the basic course of mathematical analysis is given to Riemann integral, including Lebesgue Theorem and Fubini Theorem, partition of unity and change of variables, differential forms and Stokes Theorem for manifolds.
- Syllabus
- 1. Riemann integral (divisions, null sets, oscillation, Lebesgue Theorem on Riemann integral, Fubini Theorem, partition of unity, change of variables in integral).
2. Differential forms (tensors, antisymmetric tensors, differential forms, exterior differential).
3. Stokes Theorem (chains, integral over a chain, Stokes Theorem for chains, manifolds, tangent space, orientation, Stokes Theorem for manifolds, theorems on rotor and on divergence).
4. Elements of comlex analysis (functions of one comlex variable, derivative and integral for such functions, Cauchy formula, residues).
5. Ordinary differential equations (Theorem on existence and uniqueness of the solution, methods of solutions, linear equations).
- 1. Riemann integral (divisions, null sets, oscillation, Lebesgue Theorem on Riemann integral, Fubini Theorem, partition of unity, change of variables in integral).
- Literature
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Enrolment Statistics (Summer 2016, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2016/MU01004