SubjectsSubjects(version: 865)
Course, academic year 2019/2020
Mathematics A - AB413001
Title: Mathematics A
Guaranteed by: Department of Mathematics (413)
Actual: from 2019 to 2019
Semester: winter
Points: winter s.:8
E-Credits: winter s.:8
Examination process: winter s.:
Hours per week, examination: winter s.:3/4 C+Ex [hours/week]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Language: English
Teaching methods: full-time
For type: Bachelor's
Additional information:
Old code: M1
Note: enabled for web enrollment
Guarantor: Maxová Jana RNDr. Ph.D.
Axmann Šimon Mgr. Ph.D.
Class: Předměty pro matematiku
Interchangeability : B413001, N413002, N413022
Z//Is interchangeable with: B413001
Annotation -
Last update: Kubová Petra Ing. (06.03.2019)
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: Kubová Petra Ing. (06.03.2019)

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).

Literature -
Last update: Kubová Petra Ing. (06.03.2019)

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

Learning resources -
Last update: Kubová Petra Ing. (06.03.2019)

Teaching methods -
Last update: Kubová Petra Ing. (06.03.2019)

Lectures and seminars

Requirements to the exam -
Last update: Maxová Jana RNDr. Ph.D. (27.05.2019)

It is necessary to pass two tests during the semester or to pass a comprehensive test. Another condition for granting the credit is the completion of the entrance test. The exam is combined - written and oral.

Syllabus -
Last update: Kubová Petra Ing. (06.03.2019)

1. Functions of a single real variable. Domain and range. Graphs of elementary functions. Basic properties. Composition of functions.

2. Inverse functions. Exponential and logarithmic functions. Trigonometric and inverse trigonometric functions.

3. Continuity of a function. Properties of continuous functions. Limits of sequences and functions.

4. Derivatives. Geometrical and physical meaning of derivatives. Rules for computing derivatives. Differential of a function.

5. Physical and geometrical applications of derivatives. L’Hospital’s rule. Approximation of a function value using Taylor polynomial. Analysis and graphing of a function.

6. Numerical solution of an equation of a single uknown variable - Newton’s method.

7. Antiderivatives and their properties. Newton definite integral, its properties and geometrical meaning.

8. Methods for computing indefinite and definite integrals – integration by parts and substitution method.

9. Integration of rational functions. Improper integrals. Numerical integration – trapezoidal method.

10. Definition of definite integral in physics – Riemann integral. Selected geometrical and physical applications of the integral.

11. Differential equations. Terminology, general and particular solution. Separation of variables.

12. First order linear differential equations. Variation of constants. Numerical solution of a first order differential equations – Euler’s method.

13. First and second order linear differential equations with constant coefficients and a special right-hand. Estimation method.

14. Application of differential equations in Physics, Chemistry, and Biochemistry. Revision and discussion.

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (09.05.2019)

No requirements.

Course completion requirements -
Last update: Maxová Jana RNDr. Ph.D. (27.05.2019)

It is necessary to pass two control tests during the semester, eventually to pass an additional comprehensive test successfully. Attendance at seminars is compulsory. Another condition for granting the credit is the completion of the entrance test.

Credit granted is a necessary condition for passing the exam. The exam is combined - written and oral.

Teaching methods
Activity Credits Hours
Konzultace s vyučujícími 0,5 14
Účast na přednáškách 1,5 42
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 2 56
Příprava na zkoušku a její absolvování 2 56
Účast na seminářích 2 56
8 / 8 224 / 224
Coursework assessment
Form Significance
Examination test 40
Continuous assessment of study performance and course -credit tests 20
Oral examination 40