Anotace

Sylabus

• Extreme points of a function.
• Antiderivative and indefinite integral. Integration by parts, a method of substitution.
• Definite integral and its applications.
• Sequences and infinite number series, various criteria for convergence of a series.
• Sequences and series of functions, power series.
• Approximation of a function, Taylor polynomial, Taylor series.
• Fourier series
• Introduction to the theory of complex functions of one complex variable
• Monotony, convexity, and concavity of a function.
• Mean value theorems, 1'Hospital's rule, asymptotes of a function.
• Derivative, geometric and physical interpretation of the first derivative, calculation of derivatives.
• Limit and continuity of a function.
• Real and complex functions of one real variable, elementary functions.
• Basic facts from the propositional logic and the set theory.

Doporučená literatura

• HERMAN, Edwin, STRANG, Gilbert. Calculus Volume 1, Open Stax 2020, ISBN-13: 978-1-947172-13-5
• HERMAN, Edwin, STRANG, Gilbert. Calculus Volume 2, Open Stax 2020, ISBN-13: 978-1-947172-14-2
• BHALA Rajendra:Fourier series, Mathematical Association of America, 2012
• OBERGUGGEBERGER Michael, OSTEMANN Alexander. Analysis for computer scientists, Springer, London, Dordrecht, Heidelberg, New York, 2011
• ADAMS, Robert A.: Calculus: a complete course (9th edition), Pearson, Addison Wesley, Toronto, 2017
• LANG Sergie. A first course in calculus (5th edition) Springer, London, 1998
• learning support in LMS Moodle