SubjectsSubjects(version: 863)
Course, academic year 2019/2020
Mathematics B - AB413002
Title: Mathematics B
Guaranteed by: Department of Mathematics (413)
Actual: from 2019 to 2019
Semester: summer
Points: summer s.:7
E-Credits: summer s.:7
Examination process: summer s.:
Hours per week, examination: summer s.:3/3 C+Ex [hours/week]
Capacity: unknown / unknown (1000)
Min. number of students: unlimited
Language: English
Teaching methods: full-time
For type: Bachelor's
Additional information:
Old code: M2
Note: enabled for web enrollment
Guarantor: Axmann Šimon Mgr. Ph.D.
Maxová Jana RNDr. Ph.D.
Class: Předměty pro matematiku
Interchangeability : B413002, N413003, N413003A, N413021, S413003
Z//Is interchangeable with: B413002
Annotation -
Last update: Kubová Petra Ing. (06.03.2019)
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: Kubová Petra Ing. (06.03.2019)

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: Kubová Petra Ing. (06.03.2019)

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

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

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

Přednášky a cvičení

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. The exam is combined - written and oral.

Syllabus -
Last update: Maxová Jana RNDr. Ph.D. (18.02.2020)

1. Vectors and matrices, matrix arithmetic, dot product. Linear independence of vectors and rank of a matrix.

2. Systems of linear algebraic equations. Determinant of a matrix, cross product.

3. Inverse matrices. Eigenvalues of a matrix. Geometry in the plane and three-dimensional space.

4. Euclidean space, metric, norm, properties of subsets of the Eucidean space.

5. Functions of several variables. Partial derivatives, partial derivatives of compositions of functions. Directional derivatives, gradient of a function. Total differential, tangent plane.

6. Taylor polynomial of functions of two variables. Newton’s method for a system of two non-linear equations of two variables.

7. Extrema of functions of two variables. Least square method.

8. Implicitly defined functions of a single and several variables, derivatives of implicitly defined functions.

9. Parametric curves, tangent vector to a curve, smooth curve, orientation and a sum of curves.

10. Vector field in the plane and space. Curvilinear integral of a vector field and its physical meaning.

11. Path independence of the curvilinear integral of a vector field. Scalar potential of a vector field. Differential forms and their integrals.

12. Double integral and its geometrical meaning. Fubini theorem. Substitution for double integral. Polar coordinates.

13. Laplace integral. Revision and discussion.

14. Systems of two first order differential equations. Solving autonomous systems of differential equations with constant coefficients. Predator-prey model.

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (03.05.2019)

Mathematics A

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.

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 1,5 42
Příprava na zkoušku a její absolvování 2 56
Účast na seminářích 1,5 42
7 / 7 196 / 196
Coursework assessment
Form Significance
Examination test 40
Continuous assessment of study performance and course -credit tests 20
Oral examination 40