Course: Mathematical Analysis 1

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Course title Mathematical Analysis 1
Course code KMA/MA1M
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 10
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.
  • Andres Jan, prof. RNDr. dr hab. DSc.
  • Machalová Jitka, RNDr. Ph.D.
  • Tomeček Jan, doc. RNDr. Ph.D.
Course content
1. Real numbers. Supremum and infimum of a set. The supremum theorem. The topology of real numbers. 2. Sequences of real numbers. Limits of sequences. Subsequences. Number e. 3. Functions of a single real variable. Global and local properties of functions. Elementary functions. 4. Limits of functions. Theorems on limits. 5. Continuity of real functions. Basic theorems. Functions continuous on an interval. Equicontinuity of functions. 6. Derivative of a function, definition and application. Derivatives of higher orders. 7. The Fermat theorem. 8. Basic theorems of the differential calculus - the Rolle theorem, the Lagrange theorem and the Cauchy theorem. 9. The L´Hospital rule. 10. Taylor and Maclaurin polynomials, theorems on remainders. 11. Taylor and Maclaurin series. 12. Sketching graphs of functions using derivatives.

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 - 40 hours per semester
  • Preparation for the Course Credit - 65 hours per semester
  • Preparation for the Exam - 120 hours per semester
Learning outcomes
To understand the fundamentals of diferential calculus of functions of a single variable.
Comprehension Understand the mathematical tools of diferential calculus of functions of a single variable.
Prerequisites
Grammar school mathematics.

Assessment methods and criteria
Oral exam, Written exam

Credit: the student has to pass three written tests (i.e. obtain at least half of the possible points in each test). Exam: the student has to pass a written test, understand the subject and be able to prove the principal results.
Recommended literature
  • Kojecká J., Kojecký T. (2001). Matematická analýza I. Skriptum UP Olomouc.
  • Kojecká J., Závodný M. (2003). Příklady z MA I. Skriptum UP Olomouc.
  • Rudin, W. (1964). Principles of Mathematical Analysis. McGraw-Hill.


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