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Course, academic year 2023/2024
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Calculus Ib - NMAA072
Title: Kalkulus Ib
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: summer
E-Credits: 8
Hours per week, examination: summer s.:4/2, 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
Classification: Mathematics > Real and Complex Analysis
Interchangeability : NMAA002, NMMA112
Is incompatible with: NMMA112, NMMA122
Is interchangeable with: NMMA112, NMMA122
Annotation -
Integral of real functions of one variable, differential equations, functions of more variables.
Last update: T_KMA (15.05.2003)
Literature - Czech

V.Jarník: Integrální počet I

J.Milota: Matematická analýza I, II (skripta)

J.Kopáček: Matematika pro fyziky II (skripta)

J.Veselý: Matematická analýza pro učitele I,II (skripta)

Last update: T_KMA (13.05.2003)
Syllabus -

1. Integral of real functions of one variable: indefinite integral (antiderivative), definite integrals (Riemann and Newton), calculation of integrals (by parts, substitution, integration of rational and similar functions), convergence of definite integrals.

2. Applications of integrals: integral criterion for convergence of series, area between curves, volumes of solids, length of plane curves, area of surfaces of revolution, moments and centers of mass.

3. Diferential equations: existence theorems, separation of variables, linear differential equations, systems of linear differential equations, applications of differential equations in geometry, physics and elsewhere, stability of solutions.

4. Functions of more variables: limits, continuity, partial derivatives, polar and spherical coordinates, theorems on continuous functions and implicit functions, maxima and minima, integrals, examples of partial differential equations.

Last update: T_KMA (13.05.2003)
 
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