Course detail

# Calculus 1

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

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.

Recommended optional programme components

Not applicable.

Recommended or required reading

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.

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.

Language of instruction

Czech, English

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.

Classification of course in study plans

• Programme BIT Bachelor's, 1. year of study, summer semester, 4 credits, compulsory

• Programme IT-BC-3 Bachelor's

branch BIT , 1. year of study, summer semester, 4 credits, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

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 hours, compulsory

Teacher / Lecturer

Syllabus

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

E-learning texts

Krupková, V., Fuchs, P., Matematická analýza pro FIT (cs)
Fajmon, B., Hlavičková, I., Novák, M., Vítovec, J., Numerická matematika a pravděpodobnost (cs)
Kolářová, E., Matematika 1 - Sbírka úloh (cs)
Krupková, V., Matematický seminář pro FIT (cs)
Novák, M., Matematika 3 - Sbírka příkladů z numerických metod (cs)