Mathematical Analysis 1

Language of Instruction:Czech
Completion:credit+exam (written)
Type of
Guarantor:Fuchs Petr, RNDr., Ph.D. (DMAT)
Deputy guarantor:Hliněná Dana, doc. RNDr., Ph.D. (DMAT)
Lecturer:Fuchs Petr, RNDr., Ph.D. (DMAT)
Hliněná Dana, doc. RNDr., Ph.D. (DMAT)
Instructor:Fuchs Petr, RNDr., Ph.D. (DMAT)
Hliněná Dana, doc. RNDr., Ph.D. (DMAT)
Vítovec Jiří, Mgr., Ph.D. (DMAT)
Faculty:Faculty of Electrical Engineering and Communication BUT
Department:Department of Mathematics FEEC BUT
Discrete Mathematics (IDM), DMAT
Mathematical Analysis 2 (IMA2), DMAT
Substitute for:
Mathematical Analysis (IMA), DMAT
Monlecture - FuchslecturesD105 09:0010:501BIB 2BIA 2BIB xx
Tuelecture - HliněnálecturesD0206 D105 13:0014:501BIA 2BIA 2BIB xx
Tuecomp.lab - HliněnálecturesA113 15:0016:501BIA 2BIA 2BIB xx
Wedcomp.lab - HliněnálecturesA113 11:0012:501BIB 2BIA 2BIB xx
Wedcomp.lab - FuchslecturesA113 14:0015:501BIA 2BIA 2BIB xx
Wedcomp.lab - FuchslecturesA113 16:0017:501BIA 2BIA 2BIB xx
Thucomp.lab - HliněnálecturesA113 08:0009:501BIA 2BIA 2BIB xx
Thucomp.lab - HliněnálecturesA113 10:0011:501BIB 2BIA 2BIB xx
Thucomp.lab - VítoveclecturesA113 14:0015:501BIA 2BIA 2BIB xx
Thucomp.lab - VítoveclecturesA113 16:0017:501BIA 2BIA 2BIB xx
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.
  Limit, continuity and derivative of a function. Extrema and graph properties. Approximation and interpolation. Indefinite and definite integrals.
Knowledge and skills required for the course:
  Secondary school mathematics.
Learning outcomes and competencies:
  The ability to understand the basic problems of calculus and use derivatives and integrals for solving specific problems.
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.
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.
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.
Study literature:
  • Krupková, V., Fuchs, P., Matematická analýza pro FIT, elektronický učební text, 2013. (in Czech).
Controlled instruction:
  Classes are compulsory (presence at lectures, however, will not be controlled), absence at numerical classes has to be excused.
Progress assessment:
  Written tests during the semester (maximum 30 points).
Exam prerequisites:
  At least 10 points from the tests during the semester.

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