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Course, academic year 2023/2024
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Applications of Mathematics for Teachers - NMUM461
Title: Aplikace matematiky pro učitele
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: summer
E-Credits: 2
Hours per week, examination: summer s.:0/2, colloquium [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: Mgr. Zdeněk Halas, DiS., Ph.D.
Class: Učitelství matematiky
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Teaching > Mathematics
Annotation -
Last update: T_KDM (04.05.2015)
In the first three years of the teaching branch of study in mathematics student gains valuable knowledge of theory - this is a good base for starting to get acquainted with real applications - with concrete examples of adoption of mathematics. This seminar is a good platform for computation, simulation or simply familiarization with applications. No preliminary knowledge of physics is required.
Aim of the course -
Last update: Mgr. Zdeněk Halas, DiS., Ph.D. (05.10.2017)

To give to future teachers support in grasping real applications of mathematics, offer them interesting and concrete examples of real applications and impulses for enhancing theirs and their future students positive approach to mathematics.

Course completion requirements -
Last update: Mgr. Zdeněk Halas, DiS., Ph.D. (29.10.2019)

The condition for completing the course: written test (applications of mathematics to the extent discussed in the seminar).

A maximum of two absences may be tolerated.

Literature -
Last update: T_KDM (04.05.2015)

Rektorys, K. a kol. Přehled užité matematiky I, II. Prometheus, 2000.

Rektorys, K. Co je a k čemu je vyšší matematika. Academia, 2001.

Schwalbe, D., Wagon, S. Visualizing Differential Equations with Mathematica. Springer, 1997.

Gray, A., Mezzino, M., Pinsky, M. A. Introduction to Ordinary Differential Equations with Mathematica. Springer, 1997.

Syllabus -
Last update: T_KDM (04.05.2015)

1. In the beginning: concept of derivative and its direct applications.

2. Carbon dating.

3. Textbook examples of applications of differential equations: population growth, spread of a disease, polluting;

geometric problems: parabolic mirror;

selected applications of DE in economy;

circuits; orthogonal and izogonal trajectories;

4. Motion of celestial bodies - exact calculations and computer simulation. Dating of historical events.

5. Mass, space and time - geometry of real space.

6. Remarkable applications of differential geometry.

7. Partial differential equations: basic classification, boundary conditions, applications of PDE. Heat equation - simulation in Mathematica.

8. Simulation of flows - pump, wings. Infinite dimension spaces.

9. Weather and chaos. Strange behavior of solutions of some differential equations.

10. Architecture and geometry. Shell constructions.

11. Beams and bridges.

12. Statistics: scientific data evaluation; statistics and press canards.

13. Algorithms in calculators.

14. Image processing, focusing and other effects - digital photos. Signal transmission.

15. Equations with impulses - artificial heart.

 
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