Course details

Calculus 2

IMA2 Acad. year 2020/2021 Winter semester 4 credits

Series. The limit, continuity, partial derivatives and extrema of a function of several variables. Double and triple integrals. Differential equations. Analytical and numerical solutions of the initial problem.

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

80 exam, 20 exercises

Department

Department of Mathematics (DMAT FEEC BUT)

Lecturer

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

Instructor

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

Subject specific learning outcomes and competences

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

Learning objectives

The main goal of the course is to enhance the knowledge of calculus from the previous semester and explain the basic principles and methods of higher calculus. The emphasis is put on handling the practical use of these methods for solving specific problems.

Why is the course taught

The IMA2 course follows on the IMA1 course and complements the necessary knowledge of the concepts of calculus needed to understand and master advanced technical and physical subjects.

Prerequisites

Prerequisite kwnowledge and skills

The IMA1 course.

Study literature

  • Krupková, V., Fuchs, P., Matematická analýza pro FIT, elektronický učební text, 2019.

Fundamental literature

  • Knichal, V., Bašta, A., Pišl, M., Rektorys, K., Matematika I, II, SNTL Praha, 1966.
  • 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), McGraw-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. Number series.
  2. Power series.
  3. Fourier series. Fourier transform.
  4. Differential calculus of functions of several variables I: limit, continuity, partial derivatives, Schwarz theorem.
  5. Differential calculus of functions of several variables II: differential, tangent plane, Taylor polynomial.
  6. Differential calculus of functions of more variables III: local extrema, Hess matrix, Sylvester criterion,.
  7. Integral calculus of functions of several variables I: double integral, normal domain in plane, Fubini's theorem, change of variables.
  8. Integral calculus of functions of several variables II: triple integral, normal domain in space, Fubini's theorem.
  9. Integral calculus of functions of several variables III: change of variables in triple integral.
  10. Introduction to differential equations. Initial problem. Existence and uniqueness of a solution. Separable equation. Linear equation
  11. Numerical solution of differential equations of the first order.

Syllabus of numerical exercises

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

Progress assessment

Home assignments during the semester.

Controlled instruction

Classes are not compulsory.

Exam prerequisites

The condition for receiving the credit is obtaining at least a given minimum of points from the activities during the semester.

Schedule

DayTypeWeeksRoomStartEndLect.grpGroupsInfo
Monexam2021-01-25 A112 A113 A218 C228 D0206 D0207 D105 E104 E105 E112 G108 G202 M103 M104 M105 N103 N104 N105 N203 N204 N205 O204 S206 T10/1.36 T8/010 T8/020 T8/030 09:0010:50 2BIA 2BIB 3BIT 1. oprava
Monexerciselectures T8/302 09:0010:50 2BIA 2BIB 3BIT xx Vítovec
Monlecturelectures D105 09:0010:50 2BIA 3BIT xx Fuchs
Monlecture3., 4., 5., 6., 7., 8., 9., 10., 11., 12. of lectures D105v 09:0010:50YT, ZP, Fuchs
Monexam2021-01-25 A218 G108 O204 S206 11:0012:50 2BIA 2BIB 1. oprava
Monlecturelectures T12/2.173 11:0012:50 2BIB 3BIT xx Vítovec
Monexerciselectures D0207 12:0013:50 2BIA 2BIB 3BIT xx Fuchs
Monexercise3., 4., 5., 6., 7., 8., 9., 10., 11., 12. of lectures D0207v 12:0013:50YT, ZP, bez projekce; Vítovec
Monexerciselectures D0207 14:0015:50 2BIA 2BIB 3BIT xx Fuchs
Tueexerciselectures D0207 08:0009:50 2BIA 2BIB 3BIT xx Vítovec
Tueexam2021-01-05 A112 A113 A218 C228 D0206 D0207 D105 E104 E105 E112 G108 G202 L314 M103 M104 M105 N103 N104 N105 N203 N204 N205 O204 T10/1.36 T8/010 T8/020 T8/030 09:0010:50 2BIA 2BIB 3BIT řádná
Tueexerciselectures D0207 10:0011:50 2BIA 2BIB 3BIT xx Vítovec
Tueexam2021-01-05 A112 A113 A218 C228 D0206 D0207 D105 E105 E112 G108 G202 L314 M103 M104 M105 N103 N104 N105 N203 N204 N205 O204 11:0012:50 2BIA 2BIB 3BIT řádná
Wedexerciselectures T8/302 13:0014:50 2BIA 2BIB 3BIT xx Fuchs
Wedexerciselectures T8/235 15:0016:50 2BIA 2BIB 3BIT xx Vítovec
Wedexerciselectures T8/302 15:0016:50 2BIA 2BIB 3BIT xx Fuchs
Wedexerciselectures T8/235 17:0018:50 2BIA 2BIB 3BIT xx Vítovec
Thuexam2021-02-04 G108 L314 M103 M104 M105 N103 N104 N105 N203 N204 N205 O204 T8/010 T8/020 T8/030 12:0013:50 2BIA 2BIB 3BIT 2. oprava

Course inclusion in study plans

  • Programme BIT, 2nd year of study, Compulsory
  • Programme IT-BC-3, field BIT, 2nd year of study, Compulsory
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