Faculty of Information Technology, BUT

Course details

Mathematical Analysis

IMA Acad. year 2018/2019 Summer semester 6 credits

Limit and continuity, derivative of a function. Partial derivatives. Basic differentiation rules. Elementary functions. Extrema for functions (of one and of several variables). Indefinite integral. Techniques of integration. The Riemann (definite) integral. Multiple integrals. Applications of integrals. Infinite sequences and infinite series. Taylor polynomials.

Guarantor

Deputy Guarantor

Language of instruction

Czech

Completion

Examination (written)

Time span

39 hrs lectures, 20 hrs pc labs, 6 hrs projects

Assessment points

60 exam, 28 half-term test, 12 projects

Department

Lecturer

Instructor

Subject specific learning outcomes and competences

The ability of orientation in the basic problems of higher mathematics and the ability to apply the basic methods. Solving problems in the areas cited in the annotation above by using basic rules. Solving these problems by using modern mathematical software.

Learning objectives

The main goal of the calculus course is to explain the basic principles and methods of higher mathematics that are necessary for the study of computer science. The practical aspects of applications of these methods and their use in solving concrete problems (including the application of contemporary mathematical software in the laboratories) are emphasized.

Prerequisite kwnowledge and skills

Secondary school mathematics and the kowledge from Discrete Mathematics course.

Study literature

  • Brabec B., Hrůza,B., Matematická analýza II, SNTL, Praha, 1986.
  • Švarc, S. a kol., Matematická analýza I, PC DIR, Brno, 1997.
  • Krupková, V. Matematická analýza pro FIT, electronical textbook, 2007.

Fundamental literature

  • 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.
  • Zill, D.G., A First Course in Differential Equations, PWS-Kent Publ. Comp., 1992.

Syllabus of lectures

  1. Function of one variable, limit, continuity.
  2. Differential calculus of functions of one variable I: derivative, differential, Taylor theorem.
  3. Differential calculus of functions of one variable II: maximum, minimum, behaviour of the function.
  4. Integral calculus of functions of one variable I: indefinite integral, basic methods of integration.
  5. Integral calculus of functions of one variable II: definite Riemann integral and its application.
  6. Infinite number and power series.
  7. Taylor series.
  8. Functions of two and three variables, geometry and mappings in three-dimensional space.
  9. Differential calculus of functions of more variables I: directional and partial derivatives, Taylor theorem.
  10. Differential calculus of functions of more variables II: funcional extrema, absolute and bound extrema.
  11. Integral calculus of functions of more variables I: two and three-dimensional integrals.
  12. Integral calculus of functions of more variables II: method of substitution in two and three-dimensional integrals.

Syllabus of numerical exercises

The class work is prepared in accordance with the lecture.

Syllabus - others, projects and individual work of students

  • Limit, continuity and derivative of a function. Partial derivative. Derivative of a composite function.
  • Differential of function of one and several variables. L'Hospital's rule. Behaviour of continuous and differentiable function. Extrema of functions of one and several variables.
  • Primitive function and undefinite integral. Basic methods of integration. Definite one-dimensional and multidimensional integral.
  • Methods for solution of definite integrals (Newton-Leibnitz formula, Fubini theorem).
  • Indefinite number series. Convergence of series. Sequences and series of functions. Taylor theorem. Power series.

Progress assessment

Practice tasks: 28 points.
Homeworks: 12 points.
Semestral examination: 60 points.

Schedule

DayTypeWeeksRoomStartEndLect.grpGroupsInfo
Monlecturelectures T12/2.173 08:0010:50 1BIB 2BIA 2BIB xx Vítovec
Moncomp.lablectures T8/503 14:0015:50 1BIA 2BIA 2BIB xx 10 - 11 Fuchs
Moncomp.lablectures T8/503 16:0017:50 1BIA 2BIA 2BIB xx 12 - 13 Fuchs
Tuecomp.lablectures T8/522 10:0011:50 1BIB 2BIA 2BIB xx 30 - 31 Fusek
Tuecomp.lablectures T8/522 12:0013:50 1BIB 2BIA 2BIB xx 32 - 33 Fusek
Tuelecturelectures D105 13:0015:50 1BIA 2BIA 2BIB xx Hliněná
Wedcomp.lablectures T8/503 08:0009:50 1BIB 2BIA 2BIB xx 38 - 39 Fusek
Wedcomp.lablectures T8/522 08:0009:50 1BIB 2BIA 2BIB xx 34 - 35 Novák
Wedcomp.lablectures T8/503 10:0011:50 1BIB 2BIA 2BIB xx 40 - 41 Fuchs
Wedcomp.lablectures T8/522 10:0011:50 1BIB 2BIA 2BIB xx 36 - 37 Vítovec pokročilé
Wedexam2019-05-29 D105 T10/1.36 12:0013:50 1BIA 1BIB 2BIA 2BIB 10 - 21 30 - 37 1. oprava
Wedcomp.lablectures A113 N103 N104 N105 12:0013:50 1BIA 2BIA 2BIB xx 14 - 15 Hliněná pokročilé
Wedcomp.lablectures A113 N103 N104 N105 14:0015:50 1BIA 2BIA 2BIB xx 16 - 17 Hliněná
Thuexam2019-05-09 T12/2.173 12:0014:50 1BIB 34 - 41 řádná - cv. St. od 8:00 a 10:00
Thuexam2019-05-09 T10/1.36 12:0014:50 2BIB řádná - cv. Út. od 10:00 a 12:00
Thuexam2019-05-09 T12/2.173 12:0014:50 2BIB řádná - cv. St. od 8:00 a 10:00
Thuexam2019-05-09 D105 12:0014:50 1BIA 14 - 17 řádná - cv. St. od 14:00 a 17:00
Thuexam2019-05-09 D0207 12:0014:50 2BIA řádná - cv. Pondělí od 14:00
Thuexam2019-05-09 D105 12:0014:50 1BIA 12 - 13 řádná - cv. Pondělí od 16:00
Thuexam2019-05-09 D105 12:0014:50 2BIA řádná - cv. Po od 16:00 St od 12
Thuexam2019-05-09 T10/1.36 12:0014:50 1BIB 30 - 33 řádná - cv. Út. od 10:00 a 12:00
Thuexam2019-05-09 D0206 12:0014:50 2BIA řádná - cv. Pá. od 8:00 a 10:00
Thuexam2019-05-09 D0207 12:0014:50 1BIA 10 - 11 řádná - cv. Pondělí od 14:00
Thuexam2019-05-09 D0206 12:0014:50 1BIA 18 - 21 řádná - cv. Pá. od 8:00 a 10:00
Fricomp.lablectures T8/522 08:0009:50 1BIA 2BIA 2BIB xx 18 - 19 Fusek
Fricomp.lablectures T8/522 10:0011:50 1BIA 2BIA 2BIB xx 20 - 21 Fusek
Friexam2019-06-07 D0206 T8/010 12:0013:50 1BIA 1BIB 2BIA 2BIB 2. oprava
Friexam2019-05-03 D105 13:0014:50 1BIA 1BIB 2BIA 2BIB předtermín

Course inclusion in study plans

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