Course detail

Calculus 2

FIT-IMA2Acad. year: 2020/2021

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

RNDr. Petr Fuchs, Ph.D.

Department

Department of Mathematics (UMAT)

Learning outcomes of the course unit

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

Prerequisites

The IMA1 course.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

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

Course curriculum

Not applicable.

Work placements

Not applicable.

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.

Specification of controlled education, way of implementation and compensation for absences

Classes are not compulsory.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme BIT Bachelor's, 2. year of study, winter semester, compulsory

  • Programme IT-BC-3 Bachelor's

    branch BIT , 2. year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

RNDr. Petr Fuchs, Ph.D.
Mgr. Jiří Vítovec, Ph.D.

Syllabus

  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.

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

RNDr. Petr Fuchs, Ph.D.
Mgr. Jiří Vítovec, 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 (cs)
Fajmon, Hlavičková, Novák, Vítovec: Numerická matematika a pravděpodobnost (cs)
Kolářová: IMA 2 - Sbírka úloh (cs)