SubjectsSubjects(version: 867)
Course, academic year 2019/2020
  
Mathematical Analysis III - NMUM201
Title: Matematická analýza III
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: RNDr. Jakub Staněk, Ph.D.
RNDr. Martin Rmoutil, Ph.D.
Class: M Bc. MZV
M Bc. MZV > Povinné
M Bc. MZV > 2. ročník
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Incompatibility : NMUM815
Interchangeability : NMUM815, NUMP005
Annotation -
Last update: T_KDM (14.09.2013)
Basic course in mathematical analysis for second year students.
Course completion requirements -
Last update: RNDr. Jakub Staněk, Ph.D. (29.10.2019)

In order to get the assessment, it is necessary to pass two tests. The first one concerns convergence of series, the second one focuses on differential equations. Each test consists of three tasks. It is needed to solve at least two of the tasks to pass the test. It is necessary to get the assessment before going to the exam. The exam has both written and oral parts.

Literature -
Last update: T_KDM (29.04.2013)
  • Veselý, J. Základy matematické analýzy I. Matfyzpress, Praha, 2004.
  • Veselý, J. Základy matematické analýzy II. Matfyzpress, Praha, 2009.
  • Kopáček, J. Matematická analýza nejen pro fyziky II. Matfyzpress, Praha, 2007.
  • Kopáček, J. Příklady z matematiky nejen pro fyziky II. Matfyzpress, Praha, 2006.
  • Došlá, Z. a kol. Nekonečné řady s programem Maple. Brno, 2002. Dostupné z .
  • Černý, I. Úvod do inteligentního kalkulu 2. Academia, Praha, 2005.
  • Brabec, J. a kol. Matematická analýza I. SNTL/Alfa, Praha, 1985.
  • Brabec, J., Hrůza, B. Matematická analýza II. SNTL/Alfa, Praha, 1986.
  • Jarník, V. Diferenciální počet I. Academia, Praha, 1974.
  • Krantz, S. G. Differential Equations Demystified. McGraw-Hill, 2005.
  • Trench, W. F. Introduction to Real Analysis. Dostupné z < http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF >
  • Hairer, E., Wanner, G. Analysis by its History. Springer, 2008.

Requirements to the exam -
Last update: RNDr. Jakub Staněk, Ph.D. (29.10.2019)

The exam has both written and oral parts. First, a test is written, and if the student does not pass the test, the exam is rated as failed. If the test is passed, but the oral part of the exam is not satisfactory, the exam is rated as failed as well, and next time, the student must complete both parts of the exam. The test consists of three tasks, which correspond to the syllabus of the subject and to the examples solved at the subject exercises. It is needed to solve at least two of the tasks to pass the test. If the student solve exactly two tasks, the exam cannot be rated as excellent. Content of the oral exam corresponds to the syllabus of the subject in the extend presented in the lectures.

Syllabus -
Last update: RNDr. Martin Rmoutil, Ph.D. (11.10.2018)

Ordinary differential equations, existence and uniqueness of solutions. Basic types of first-order equations, linear differential equations of the n-th order (especially with constant coefficients).

Infinite series, absolute and nonabsolute convergence, criteria of convergence.

 
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