Description:

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

Recommended literature:

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.

Keywords:

integral calculus, real function, real variable, analysis, limit, antiderivative, Riemann integral, infinite series

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar