M3501c Mathematical Analysis III

Faculty of Science
Autumn 1999
Extent and Intensity
0/2/0. Type of Completion: z (credit).
Teacher(s)
Mgr. Pavel Blažek (seminar tutor)
RNDr. Roman Plch, Ph.D. (seminar tutor)
doc. Ing. Jiří Šremr, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Zuzana Došlá, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Josef Kalas, CSc.
Prerequisites (in Czech)
M2510 Mathematical Analysis 2 && NOW ( M3501p Mathematical Analysis III )
Course Enrolment Limitations
The course is offered to students of any study field.
Syllabus
  • Metric Spaces -- Basic concepts and properties of metric spaces, spaces $\Bbb E^n$. -- Cauchy and convergent sequences, complete spaces. -- Banach fixed point theorem and its applications. -- Continuous mappings of compact spaces. Differential Calculus of Functions of Two or More variables -- Notion of a function of two or more variables, limits, continuity (on the base of metrix spaces). -- Partial derivatives and differentiability. -- Taylor theorem. -- Local and absolute extrema. -- Implicit functions. Differential Equations -- First order differential equations, the existence--uniqueness theorem. -- Elementary methods for solving first order diferential equations and applications. -- Second order linear differential equations with constant coefficients. Infinite series of numbers: convergence, absolute and nonabsolute convergence, basic tests for convergence, operations with series.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
  • Enrolment Statistics (recent)
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