Lecturer(s)


Burkotová Jana, Mgr. Ph.D.

Tomeček Jan, doc. RNDr. Ph.D.

Machalová Jitka, RNDr. Ph.D.

Andres Jan, prof. RNDr. dr hab. DSc.

Fürst Tomáš, RNDr. Ph.D.

Course content

1. Antiderivative. Integration of rational functions. Special substitutions. 2. Riemann integral. Sufficient and necessary conditions of the existence of Riemann integral. Properties of Riemann integral. 3. Mean value theorems. 4. Fundamental theorem of calculus 5. Applications of Riemann integral 6. Improper integral and its convergence. Absolute and relative convergence. 7. Newton integral. Relationship between Newton and Riemann integral. 8. Differential equations of the first order. Differential equations of the second order with constant coefficients. Calculation of particular solution of nonhomogeneous equation by variation of constants method and method for equations with special righthand side. 9. Series. Series with nonnegative terms. Convergence criteria (Cauchy, d'Alembert, Raabe, integral criterium). Absolute and relative convergence of series. Convergence criteria (Leibniz, Abel, Dirichlet). Riemann's theorem. Double sequences and series. Product of series.

Learning activities and teaching methods

Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
 Attendace
 78 hours per semester
 Homework for Teaching
 20 hours per semester
 Preparation for the Course Credit
 45 hours per semester
 Preparation for the Exam
 100 hours per semester

Learning outcomes

To understand the fundamentals of integral calculus of functions of a single variable, differential equations of the first order and number series.
Comprehension Understand the mathematical tools of integral calculus of functions of a single variable, differential equations of the first order and number series.

Prerequisites

Differential calculus of functions of a single variable.
KMA/MA1M

Assessment methods and criteria

Oral exam, Written exam
Credit: the student has to pass four written tests (i.e. obtain at least half of the possible points in each test). Exam: the students has to pass a written test, understand the subject and be able to prove the principal results.

Recommended literature


J. Kojecká, M. Závodný. (2004). Příklady z diferenciálních rovnic I. Skriptum UP Olomouc.

J. Kojecká, M. Závodný. (2003). Příklady z MA II. Skriptum UP Olomouc.

J. Kojecká. (1991). Řešené příklady z matematické analýzy II. Skripta UP Olomouc.

J. Kuben. (1995). Obyčejné diferenciální rovnice. Skriptum UP Olomouc.

Rudin, W. (1964). Principles of Mathematical Analysis. McGrawHill.

V. Novák. (2004). Integrální počet v R. Brno, skriptum MU.
