MU01004 Mathematical Analysis IV

Mathematical Institute in Opava
Summer 2021
Extent and Intensity
3/0/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Petr Blaschke, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Málek, Ph.D.
Mathematical Institute in Opava
Timetable
Tue 8:05–10:30 RZ
Prerequisites (in Czech)
( MU20003 Mathematical Analysis III || MU01003 Mathematical Analysis III ) && NOW( MU01904 Mathematical Analysis IV - Exe ) && ! MU01104 Mathematical Analysis IV && !NOW( MU01104 Mathematical Analysis IV ) && TYP_STUDIA(B)
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 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).
Literature
    recommended literature
  • V. I. Averbuch, M. Málek. Matematická analýza III, IV. MÚ SU, Opava, 2003. URL 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
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 1998, Summer 1999, 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, Summer 2022.
  • Enrolment Statistics (Summer 2021, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2021/MU01004