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Course, academic year 2023/2024
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Mathematical Analysis IIa - NMAI049
Title: Matematická analýza IIa
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2004
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Petr Holický, CSc.
Classification: Mathematics > Real and Complex Analysis
Co-requisite : NMAI009
Interchangeability : NMAI056
Is co-requisite for: NMAI050
Is incompatible with: NMAF003, NMAF004
Annotation -
Last update: T_KMA (17.05.2001)
Introductory course for students of informatics covering differential equations, Lebesgue integral and some topics from metric spaces (completeness, connectedness and Banach fixed point theorem).
Syllabus -
Last update: T_KMA (15.05.2003)

I. Metric spaces

Completeness, connectedness, Banach contraction theorem.

II. Differential equations.

Peano and Picard theorems on the existence, respectively uniqueness, of the solution. Linear equations and systems, theorem on global existence and uniqueness for linear equations.

Particular solutions and methods of their determination: variation of constants, special right-hand sides.

III. Lebesgue integral

Riemann integral in Rn and its properties. Extension of Riemann integral, Lebesgue integral and its basic properties.

Levi and Lebesgue theorems. Fubini theorem. Regular mapping, change of variables. Continuity and differentiability of the integral depending on a parameter.

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