Lecturer(s)


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
 20 hours per semester
 Preparation for the Course Credit
 50 hours per semester
 Preparation for the Exam
 90 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. McGrawHill.
