Course: Mathematical Analysis 2

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Course title Mathematical Analysis 2
Course code KMA/MA2M
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 8
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
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 right-hand 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. McGraw-Hill.
  • V. Novák. (2004). Integrální počet v R. Brno, skriptum MU.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Discrete Mathematics (2016) Mathematics courses 1 Summer
Faculty of Science Mathematics and Applications (1) Mathematics courses 1 Summer