Course detail

Calculus 1

FIT-IMA1Acad. year: 2019/2020

Limit, continuity and derivative of a function. Extrema and graph properties. Approximation and interpolation. Indefinite and definite integrals.

Language of instruction

Czech, English

Number of ECTS credits

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 calculus and use derivatives and integrals for solving specific problems.

Prerequisites

Secondary school mathematics.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Written tests during the semester (maximum 30 points).

Exam prerequisites:
The condition for receiving the credit is active work during the semestr and obtaining at least 10 points from the tests during the semester.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The main goal of the course is to explain the basic principles and methods of calculus. The emphasis is put on handling the practical use of these methods for solving specific tasks.

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

Classes are compulsory (presence at lectures, however, will not be controlled), absence at numerical classes has to be excused.

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 1 year of study, summer semester, compulsory

  • Programme IT-BC-3 Bachelor's

    branch BIT , 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. RNDr. Dana Hliněná, Ph.D.
RNDr. Petr Fuchs, Ph.D.

Syllabus

  1. The concept of a function of a real variable. Properties of functions and basic operations with functions.
  2. Elementary functions of a real variable.
  3. Limit and continuity of a function. Limit of a sequence.
  4. Differential calculus of functions of one variable. Derivative at a point, derivative in an interval, a differential of a function. Numerical differentiation.
  5. Higher-order derivatives. Extrema of a function and inflection points.
  6. Graph sketching.
  7. Taylor theorem. Newton and Lagrange interpolation.
  8. Approximation. Least squares method.
  9. Numerical solutions of nonlinear equations.
  10. Integral calculus of functions of one variable. Indefinite integral, basic methods of integration.
  11. Definite Riemann integral and its applications. Numerical integration.
  12. Improper integral.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

Ing. Michal Fusek, Ph.D.
Mgr. Irena Hlavičková, Ph.D.
Mgr. Jiří Vítovec, Ph.D.
RNDr. Petr Fuchs, Ph.D.
doc. RNDr. Dana Hliněná, 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: Matematika 1 - Sbírka úloh
Matematika_1_sbirka.pdf 0.45 MB
Novák: Matematika 3 - Sbírka příkladů z numerických metod
Matematika_3_num.pdf 0.28 MB