SubjectsSubjects(version: 954)
Course, academic year 2023/2024
  
Mathematics B - B413002
Title: Matematika B
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2023 to 2023
Semester: both
Points: 7
E-Credits: 7
Examination process:
Hours per week, examination: 3/3, C+Ex [HT]
Capacity: winter:160 / 174 (1400)
summer:unknown / unknown (1400)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Level:  
Additional information: https://um.vscht.cz/studium/predmetycs
Old code: M2
Note: course can be enrolled in outside the study plan
enabled for web enrollment
you can enroll for the course in winter and in summer semester
Guarantor: Axmann Šimon Mgr. Ph.D.
Class: Předměty pro matematiku
Interchangeability : AB413002, N413003, N413003A, N413021, S413003
Is interchangeable with: N413021, AB413002
This subject contains the following additional online materials
Annotation -
The course develops and strengthens the concepts and skills of elementary mathematics (the course of mathematics MA), particularly the skills related to various disciplines of the curriculum of the master's study.
Last update: MAXOVAJ (21.09.2020)
Aim of the course -

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)

Last update: Kubová Petra (02.12.2017)
Literature -

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

Last update: Kubová Petra (02.12.2017)
Learning resources -

http://www.vscht.cz/mat/El_pom/sbirka/sbirka2.html

http://www.vscht.cz/mat/El_pom/Mat_MATH_MAPLE.html

Last update: Kubová Petra (02.12.2017)
Teaching methods - Czech

Přednášky a cvičení

Last update: Kubová Petra (02.12.2017)
Requirements to the exam - Czech

K udělení zápočtu je nutné splnit podmínky účasti na cvičeních a dva kontrolní testy v průběhu semestru, případně úspěšně absolvovat souhrnný test. Udělený zápočet je nutnou podmínkou pro skládání zkoušky. Zkouška je kombinovaná — písemná a ústní. Bližší informace viz https://um.vscht.cz/studium/predmetycs/podminky

Last update: Axmann Šimon (22.07.2022)
Syllabus -

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. Orthogonal projection of vector.

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.

Last update: Axmann Šimon (13.06.2024)
Registration requirements -

Mathematics A

Last update: Borská Lucie (03.05.2019)
Course completion requirements - Czech

K udělení zápočtu je nutné splnit podmínky účasti na cvičeních a dva kontrolní testy v průběhu semestru, případně úspěšně absolvovat souhrnný test. Udělený zápočet je nutnou podmínkou pro skládání zkoušky. Zkouška je kombinovaná — písemná a ústní. Bližší informace viz https://um.vscht.cz/studium/predmetycs/podminky

Last update: Axmann Šimon (22.07.2022)
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
 
VŠCHT Praha