Course detail

Mathematical Analysis 2

FIT-IMA2Acad. year: 2024/2025

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.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

doc. RNDr. Edita Kolářová, Ph.D.

Department

Department of Mathematics (UMAT)

Entry knowledge

The IMA1 course.

Rules for evaluation and completion of the course

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.

Aims

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.

Study aids

Not applicable.

Prerequisites and corequisites

Basic literature

Not applicable.

Recommended reading

Knichal, V., Bašta, A., Pišl, M., Rektorys, K., Matematika I, II, SNTL Praha, 1966. (CS)

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme BIT Bachelor's 2 year of study, winter semester, compulsory
  • Programme BIT Bachelor's 2 year of study, winter semester, compulsory
  • Programme IT-CZV-1 Lifelong learning 1 year of study, winter semester, elective

Type of course unit

 

Lecture

26 hod., compulsory

Teacher / Lecturer

Mgr. Jiří Vítovec, Ph.D.
doc. RNDr. Edita Kolářová, Ph.D.

Syllabus

  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.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

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

Syllabus

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

E-learning texts

Krupková, Fuchs: Matematická analýza pro FIT
Ima.pdf 5.29 MB
Fajmon, Hlavičková, Novák, Vítovec: Numerická matematika a pravděpodobnost
Inm.pdf 2.79 MB
Kolářová: IMA 2 - Sbírka úloh
IMA_2_sbirka.pdf 0.52 MB

Elearning

eLearning: currently opened course