Calculus 2

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Department of Mathematics

Synopsis:

1. Continuation of differential calculus: Taylor´s Polynomials, Taylor´s formula

2. Infinite series: criteria of convergence, operations on series, absolute and conditional convergence

3. Real and complex power series, the Cauchy-Hadamard theorem, expansion of function into power series, summation of infinite series.

4. Theory of integrals: primitives, definite integral (Riemann definition), techniques of integration and application of integrals, Generalized Riemann integral

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Povinná literatura:

[1] E. Pelantová: Matematická analýza II, skriptum ČVUT, Praha, 2015.

[2] E. Pelantová, J. Vondráčková: Cvičení z matematické analýzy (Integrální počet a řady), skriptum ČVUT, Praha, 2006.

[3] J. B. Conway: A First Course in Analysis (Cambridge Mathematical Textbooks), Cambridge University Press; 1 edition, 2017

Doporučená literatura:

[4] R. Larson, and B. H. Edwards: Calculus of a single variable: Early transcendental functions. Cengage Learning, 2014

[5] J. Stewart: Calculus, Cengage Learning, 2015.

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Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: