Course details

Mathematical Analysis 2

IMA2 Acad. year 2024/2025 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

Kolářová Edita, doc. RNDr., Ph.D. (UMAT)

Course coordinator

Fuchs Petr, RNDr., Ph.D. (UMAT)

Language of instruction

Czech, English

Completion

Credit+Examination (written)

Time span

  • 26 hrs lectures
  • 26 hrs exercises

Assessment points

  • 80 pts final exam
  • 20 pts numeric exercises

Department

Department of Mathematics (UMAT)

Lecturer

Kolářová Edita, doc. RNDr., Ph.D. (UMAT)
Vítovec Jiří, Mgr., Ph.D. (UMAT)

Instructor

Fuchs Petr, RNDr., Ph.D. (UMAT)
Kolářová Edita, doc. RNDr., Ph.D. (UMAT)
Vážanová Gabriela, Mgr., Ph.D. (UMAT)
Vítovec Jiří, Mgr., Ph.D. (UMAT)

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

Recommended prerequisites

Prerequisite knowledge and skills

The IMA1 course.

Study literature

  • 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.
  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 (particularly in 2 and 3 dimensions): definitions and basic concepts.
  8. Integral calculus of functions of several variables II: multidimensional and multiple integrals, Fubini theorem.
  9. Integral calculus of functions of several variables III: evaluation and applications of double and triple integrals.
  10. Introduction to differential equations. Initial problem. Existence and uniqueness of a solution. Separable and linear equations.
  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

Written tests during the semester (20 points for 3 tests). Classes are compulsory. Presence at lectures will not be controlled, absence at numerical classes has to be excused.

Schedule

DayTypeWeeksRoomStartEndCapacityLect.grpGroupsInfo
Mon exercise *) 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures T8/T 3.02 09:0010:500 2BIA 2BIB 3BIT xx Fuchs
Mon lecture 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures D0206 D105 09:0010:50470 2BIA 3BIT 10 - 19 xx Vítovec
Mon exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures A112 11:0012:5065 2BIA 2BIB 3BIT xx Vítovec
Mon lecture 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures Aula profesora Braunera 11:0012:50338 2BIB 3BIT 20 - 29 xx Kolářová
Mon exercise *) 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures A112 13:0014:500 2BIA 2BIB 3BIT xx Fuchs
Mon exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures A112 15:0016:5065 2BIA 2BIB 3BIT xx Vítovec
Mon exercise *) 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures A112 17:0018:500 2BIA 2BIB 3BIT xx Vítovec
Tue exercise *) 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures T8/T 3.02 09:0010:500 2BIA 2BIB 3BIT xx Kolářová
Tue exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures A113 10:0011:5065 2BIA 2BIB 3BIT xx Vážanová
Tue exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures A113 12:0013:5065 2BIA 2BIB 3BIT xx Vážanová
Tue exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures A112 15:0016:5065 2BIA 2BIB 3BIT xx Vážanová
Tue exercise *) 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures A112 17:0018:500 2BIA 2BIB 3BIT xx
Wed exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures T8/T 3.02 13:0014:5056 2BIA 2BIB 3BIT xx Fuchs
Wed exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures A112 15:0016:5065 2BIA 2BIB 3BIT xx Kolářová
Wed exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures T8/T 3.02 15:0016:5057 2BIA 2BIB 3BIT xx Fuchs
Wed exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures A112 17:0018:5065 2BIA 2BIB 3BIT xx Kolářová
Thu exercise *) 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures T8/T 3.12 11:0012:500 2BIA 2BIB 3BIT xx Kolářová
It is not possible to register this class in Studis. (Some exercises may be opened later if needed, but this is not guaranteed.)

Course inclusion in study plans

  • Programme BIT, 2nd year of study, Compulsory
  • Programme BIT (in English), 2nd year of study, Compulsory
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