Mathematics I - S413022
Title: Mathematics I
Guaranteed by: Department of Mathematics (413)
Actual: from 2020
Semester: both
Points: 10
E-Credits: 10
Examination process:
Hours per week, examination: 3/4 C+Ex [hours/week]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
Language: English
Teaching methods: full-time
Is provided by: AB413001
For type:  
Additional information: http://The course is lectured in winter semester exclusively
Note: you can enroll for the course in winter and in summer semester
Guarantor: Pokorný Pavel RNDr. Ph.D.
Examination dates   
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)
Basic course in Calculus for students in bachelor program. It provides mathematical skills necessary for other subjects (physics, physical chemistry,...) in bachelor program. Success in Mathematics I is a prerequisite for Mathematics II.
Aim of the course
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)

General skills:

1. basic mathematical terms

2. knowledge and understanding of basic algorithms

3. individual problem solving

4. basic mathematical background for formulation and solving of natural and engineering problems

5. numerical algorithms (algebraic equations, integration).

Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)

R: Porubský: Fundamental Mathematics for Engineers, Vol.I, VŠCHT, 2001, ISBN: 80-7080-418-1

Syllabus - Czech
Last update: Axmann Šimon Mgr. Ph.D. (14.01.2020)

1. Elements of Mathematical Logic. Introduction to calculus

2. Continuity and limits of the functions of one and two variables.

3. Derivatives, Mean value theorem, L’ Hospital’s rule. Partial derivatives.

4. Monotone functions, extreme values of a function, asymptotes of the graph.

5. Newton’s methods. Taylor’s formula with remainder. Differential.

6. Curves in plane, tangent vector. Polar coordinates.

7. Antiderivative. Definite integral. Geometric and physical applications.

8. Techniques of integration.

9. Improper integrals. Numerical integration. The mean value theorem for integrals.

10. Ordinary differential equations of the first order. Separable equations. Euler’s method.

11. Linear differential equations of the first and second order and their applications.

Registration requirements
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)

No requirements