SubjectsSubjects(version: 955)
Course, academic year 2023/2024
Mathematics for chemical engineers - M413007
Title: Matematika pro chemické inženýry
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2021
Semester: winter
Points: winter s.:5
E-Credits: winter s.:5
Examination process: winter s.:
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: 54 / 57 (unknown)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Janovská Drahoslava prof. RNDr. CSc.
Schreiber Igor prof. Ing. CSc.
Kočí Petr prof. Ing. Ph.D.
Class: Předměty pro matematiku
Interchangeability : AM413007, N413032
Is interchangeable with: AM413007
This subject contains the following additional online materials
Annotation -
The course builds on students' knowledge acquired in undergraduate studies. Its main focus is the study of differential equations and their systems, dynamical systems (qualitative theory), as well as a brief introduction to vector analysis and theory of partial differential equations. An integral part of this course is to practice the theoretical mathematical knowledge on specific examples from chemical engineering using advanced software.
Last update: Hladíková Jana (16.01.2018)
Aim of the course -

The aim of the course is to enable students to brush up on and deepen the knowledge acquired in undergraduate mathematics courses of study. Although students will work in the future in various fields of chemistry, they should be able to use in the formulation, analysis, and simulation results of its rigorous mathematical tools, including most advanced software available.

Last update: Hladíková Jana (16.01.2018)
Literature -

R: Turzík Daniel a kol.: Matematika II ve strukturovaném studiu, VŠCHT Praha, 2005.

A: Pavlík Jiří a kol.: Aplikovaná statistika, VŠCHT Praha, 2005.

R: Kubíček Milan, Dubcová Miroslava, Janovská Drahoslava: Numerické metody a algoritmy, VŠCHT Praha, 2005 (druhé vydání).

A: A. Klíč, M. Dubcová ,L. Buřič: Soustavy obyčejných diferenciálních rovnic, kvalitativní teorie, dynamické systémy, VŠCHT Praha, 2009, ISBN: 978-80-7080-724-8

R: Klíč Alois, Dubcová Miroslava, Buřič Lubor: Soustavy obyčejných diferenciálních rovnic, kvalitativní teorie, dynamické systémy, VŠCHT Praha, 2009.

A: Klíč Alois, Dubcová Miroslava: Základy tenzorového počtu s aplikacemi, VŠCHT Praha, 1998.

A: R.A. Horn, C.R. Johnson: Matrix Analysis. Cambridge University Press, 1999. ISBN 0-521-38632-2

Last update: Janovská Drahoslava (24.12.2021)
Learning resources -

Last update: Hladíková Jana (16.01.2018)
Teaching methods -

Lectures take place according to the syllabus. The theoretical mathematical knowledge is applied to specific tasks in chemical engineering. Matlab (namely „pplane“) is used for simulations of the behavior of dynamic systems.

Last update: Hladíková Jana (16.01.2018)
Requirements to the exam -

During the semester, students develop several miniprojects (their number depends on the difficulty of the task). On the basis of their preparation, students will gain an assessment. Without the assessment student can’t take the examination. The exam consists of a written and an oral part. For admission to the oral exam, it is necessary to gain at least 50 points from the test. If a student writes the test for the sufficient number of points and fails in the oral part, the written test need not to be repeated.

Last update: Hladíková Jana (16.01.2018)
Syllabus -

1. Basics of vector and tensor calculus. Nabla operator algebra. Grenn’s, Gauss's-Ostrogradski's theorems.

2. Surface integrals of scalar and vector fields. Gauss's and Stokes's theorems.

3. Matrix equations, inverse matrix. Eigenvalues and eigenvectors of matrices, generalized eigenvectors. Solving a system of linear algebraic equations.

4. Singular values, singular value decomposition. Least squares solution of a system of linear algebraic equations. Normal equations. Linear regression.

5. Solving systems of nonlinear equations, Newton method. Newton method for solving systems of nonlinear equations. Nonlinear regression.

6. Implicit function of one or more variables, general theorem for implicit functions.

7. Numerical solution of ordinary differential equations, initial value problem: Euler's method, Runge-Kutta methods, multistep methods.

8. Numerical solution of ordinary differential equations, boundary value problem, method of shooting.

9. Vector field, the trajectory of the system, equilibrium conditions, phase portrait. Invariant set, ω-limit sets of trajectories.

10. Systems of linear DR with constant coefficients. Phase portraits of linear systems in the plane.

11. Systems of nonlinear equations: classification of equilibrium states of nonlinear systems. Principles of construction of phase portraits in the plane. Homoclinics and heteroclinics.

12. Bifurcation. Types of bifurcations. Examples.

13. Numerical and functional series. Fourier series.

14. Classification of PDE for two independent variables. Diffusion equation and wave equation in 1-D. Fourier methods for their solution.

Last update: Janovská Drahoslava (26.12.2021)
Entry requirements -

Students are expected to have either completed the prerequisite courses Mathematics A and Mathematics B or possess the equivalent knowledge prior to enrolling in the course. Students are recommended to complete the course Numerical methods prior to enrolling in the course.

Last update: Borská Lucie (13.05.2019)
Registration requirements -

No requirements.

Last update: Borská Lucie (06.05.2019)
Teaching methods
Activity Credits Hours
Účast na přednáškách 1 28
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 1 28
Práce na individuálním projektu 1 28
Příprava na zkoušku a její absolvování 1.5 42
Účast na seminářích 0.5 14
5 / 5 140 / 140