Course details

Mathematical Analysis 1

IMA1 Acad. year 2020/2021 Summer semester 4 credits

Current academic year

Limit, continuity and derivative of a function. Extrema and graph properties. Approximation and interpolation. Indefinite and definite integrals.

Guarantor

Fuchs Petr, RNDr., Ph.D. (DMAT FEEC BUT)

Deputy Guarantor

Language of instruction

Czech

Completion

Credit+Examination (written)

Time span

26 hrs lectures, 26 hrs exercises

Assessment points

70 exam, 30 half-term test

Department

Lecturer

Fuchs Petr, RNDr., Ph.D. (DMAT FEEC BUT)

Instructor

Fuchs Petr, RNDr., Ph.D. (DMAT FEEC BUT)

Subject specific learning outcomes and competences

The ability to understand the basic problems of calculus and use derivatives and integrals for solving specific problems.

Learning objectives

The main goal of the course is to explain the basic principles and methods of calculus. The emphasis is put on handling the practical use of these methods for solving specific tasks.

Why is the course taught

Fundamentals of calculus are a necessary part of a study at a technical university because virtually all technical and physical subjects employ the concepts of a derivative and integral.

Prerequisites

Prerequisite kwnowledge and skills

Secondary school mathematics.

Study literature

  • Krupková, V., Fuchs, P., Matematická analýza pro FIT, elektronický učební text, 2013. (in Czech).

Fundamental literature

  • Knichal, V., Bašta, A., Pišl, M., Rektorys, K., Matematika I, II, SNTL Praha, 1966. (in Czech).
  • Edwards, C. H., Penney, D. E., Calculus with Analytic Geometry, Prentice Hall, 1993.
  • Fong, Y., Wang, Y., Calculus, Springer, 2000.
  • Ross, K. A., Elementary analysis: The Theory of Calculus, Springer, 2000.
  • Small, D. B., Hosack, J. M., Calculus (An Integrated Approach), Mc Graw-Hill Publ. Comp., 1990.
  • Thomas, G. B., Finney, R. L., Calculus and Analytic Geometry, Addison-Wesley Publ. Comp., 1994.

Syllabus of lectures

  1. The concept of a function of a real variable, properties of functions and basic operations with functions.
  2. Elementary functions of a real variable.
  3. Complex numbers. Functions of a complex variable.
  4. Limit of a sequence. Limit and continuity of a function.
  5. Differential calculus of functions of one variable. Derivative at a point, derivative in an interval, a differential of a function. Numerical differentiation.
  6. Second derivative. Extrema of a function.
  7. Graph properties.
  8. Taylor theorem. Approximation of functions.
  9. Newton and Lagrange interpolation.
  10. Numerical solutions of nonlinear equations.
  11. Integral calculus of functions of one variable. Indefinite integral, basic methods of integration.
  12. Definite Riemann integral, its applications.Numerical integration.
  13. Improper integral.

Syllabus of numerical exercises

Problems discussed at numerical classes are chosen so as to complement suitably the lectures.

Progress assessment

Written tests during the semester (maximum 30 points).

Controlled instruction

Classes are compulsory (presence at lectures, however, will not be controlled), absence at numerical classes has to be excused.

Exam prerequisites

At least 10 points from the tests during the semester.

Course inclusion in study plans

  • Programme BIT, 1st year of study, Compulsory
  • Programme IT-BC-3, field BIT, 1st year of study, Compulsory
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