SubjectsSubjects(version: 889)
Course, academic year 2020/2021
Mathematics II - N413003
Title: Matematika II
Guaranteed by: Department of Mathematics (413)
Actual: from 2020 to 2020
Semester: both
Points: 8
E-Credits: 8
Examination process:
Hours per week, examination: 3/3 C+Ex [hours/week]
Capacity: winter:unknown / unknown (1000)
summer:unknown / unknown (1000)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Is provided by: B413002
For type:  
Additional information:
Old code: M2
Note: you can enroll for the course repeatedly
you can enroll for the course in winter and in summer semester
Guarantor: Janovská Drahoslava prof. RNDr. CSc.
Turzík Daniel doc. RNDr. CSc.
Simerská Carmen doc. RNDr. CSc.
Class: Předměty pro matematiku
Interchangeability : S413003
Is interchangeable with: B413002, AB413002
This subject contains the following additional online materials
Annotation -
Last update: TAJ413 (17.12.2013)
The course develops and strengthens the concepts and skills of elementary mathematics (the course of mathematics MI), particularly the skills related to various disciplines of the curriculum of the master's study.
Aim of the course -
Last update: Simerská Carmen doc. RNDr. CSc. (29.08.2013)

Students will be able to:

1. use basic mathematical notions

2. know and understand basic mathematical methods

3. solve problems individually

4. gain basic knowledge of the mathematical concepts used to describe the science and engineering problems

5. get acquainted with the computational algorithms (differential equations)

Literature -
Last update: KNOBLOCL (17.12.2015)

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

Learning resources -
Last update: Simerská Carmen doc. RNDr. CSc. (29.08.2013)

Teaching methods - Czech
Last update: Turzík Daniel doc. RNDr. CSc. (19.11.2012)

Přednášky a cvičení

Syllabus -
Last update: TAJ413 (30.08.2013)

1. Geometry in R^3 (R^n). Metrics in R^n.

2. Differential calculus in R^n. Functions of two and more variables. Directional and partial derivatives. Gradient. Newton’s method.

3. Taylor’s formula. The Hessian and extreme values. Method of least squares.

4. Implicit function theory.

5. Parametric curves in the plane and in the space, vector tangent to curve, application in Physics.

6. Vector fields in R^2, R^3. Line integral of the vector field.

7. Line integrals independent of the path. Differential form, exact differential form, potential vector field.

8. Double and triple integrals. Fubini theorem.

9. Substitution in double and triple integral. Polar, cylindrical, and spherical coordinates. Improper integrals.

10. Linear space, base, dimension. Spaces R^n and C(I).

11. Linear mapping, kernel of lin. mapping, matrix representation, inverse matrix, matrix equations.

12. Differential equations, basic notions, method of separation.

13. Linear differential equations of the 1st and 2nd order. The variation of constants method.

14. The system of two linear and nonlinear dif.equations of the first order. Lotka-Wolterra system.

Registration requirements -
Last update: Simerská Carmen doc. RNDr. CSc. (29.08.2013)

Mathematics I

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 2,5 70
Příprava na zkoušku a její absolvování 2 56
Účast na seminářích 1,5 42
8 / 8 224 / 224
Coursework assessment
Form Significance
Regular attendance 10
Examination test 35
Continuous assessment of study performance and course -credit tests 20
Oral examination 35