Mathematical Analysis (KMD/E-AN1)

NOTICE: The validity of the information on this page has expired.


  • 6 credits
  • Lecturer: Ing. Tomáš Barot, Ph.D.
  • Lessons (Lectures + Exercises + Seminars): 1 + 0 + 1 [hours/week]
  • Semester: Winter / Summer
  • Language of instruction: English
  • Language of consultation: English
  • Level of qualification (Bc., Mgr.): Bc., Mgr.
  • Method of completion: Examination

Synopsis / description / annotation:

The aim of the course is to introduce basic concepts of the theory of a single variable real function. It involves a concept of real functions, basic properties of them, domain, range, graph of a function, representation of a graph function using mathematical software, limit of a function, continues functions, derivative of a function, representation of the derivative in geometry and physics, total differential of a function, local and global extrema of a function, Roll and Lagrange Theorem, course of a function.

Requirements on student:

An active participation in the full-time form of the education, an active approach to solving tasks, the successful passing of the written test of the final exam.

Content:

  1. Functions, basic concepts, properties, domain, even and odd function, increasing and decreasing function, composite function.
  2. Elementary functions – overview, parametrical systems of functions.
  3. Representation of the function graph using specialized software.
  4. The limit of a function, properties of the limit, continuity of a function.
  5. Methods of computation of the limit.
  6. The derivative of a function, the derivative of an implicit function, high order derivatives of a function, application.
  7. The total differential of a function.
  8. Bounded sets, the supremum, the infimum, Cachy and Weierstrass theorem.
  9. Fundamental theorems on differential calculus, applications of derivatives.
  10. Taylor’s Theorem, local and global extrema.
  11. Inflection points, asymptotes of the graph of a function.
  12. The course of a function.

Time requirements:

  • Being present in classes - 26 h.
  • Self-tutoring - 30 h.
  • Consultation of work with the teacher/tutor (incl. electronic) - 5 h.
  • Preparation for an exam - 30 h.

Prerequisites:

The secondary school knowledge of mathematics is assumed.

Course results:

After finishing the course, in which an understanding of topics of the mathematical analysis is offered, students will have knowledge about the advanced aspects of these parts of mathematics. Student will have abilities to solve problems using a software support for mathematics.

Assessment methods:

  • Written examination
  • Continuous analysis of student’s achievements

Teaching methods:

  • Computer-based tutoring
  • Dialogic (discussion, dialogue, brainstorming)
  • Individual tutoring

Literature:

  • Munem, M., A., Foulis, D., J. College Algebra with Applications. Worht Publishers, 1986. ISBN 0-87901-285-4.
  • Larson, R., E., Edwards, B. H. Finite Mathematics with Calculus. D. C. Heath and Company, 1991. ISBN 0-669-16804-1.

Updated: 03. 10. 2022