Czech

5

Mgr. Jana Hoderová, Ph.D.

Institute of Mathematics

Basic knowledge of mathematical analysis and linear algebra at least at the level of a bachelor's degree in a technical or science field is assumed. The student should be able to handle basic operations with vectors and matrices, work with complex numbers, differentiate and integrate functions, and use basic mathematical methods commonly applied in solving physics problems.

The course is completed with a graded credit, which is awarded based on the results of two written tests during the semester. Their purpose is to check knowledge and the ability to independently apply the mathematical methods covered in solving theoretical and practical problems.

Specific requirements for passing the test and possible makeup dates are set by the instructor and presented to students at the beginning of the semester.

The final grading follows the valid VUT grading scale.

Absence replacements

The conditions for making up missed mandatory classes are set by the teacher. The make-up assessment can take the form of a written test or another method corresponding to the content of the missed lessons.

The goal of the course is to deepen and expand students' mathematical knowledge and skills in areas used in the study of optics and related technical fields. Emphasis is placed on understanding mathematical methods, their correct use in solving physical problems, and interpreting the results obtained.

After completing the course, students will be able to:

1. Work with vector spaces, bases, dimension, and basic concepts of linear algebra.
2. Use complex numbers and complex functions in the mathematical description of physical and optical phenomena.
3. Apply differential and integral calculus of functions of one or more variables in solving mathematical and physical problems.
4. Utilize partial derivatives and selected differential operators in describing physical fields and processes.
5. Apply Fourier transformation in analyzing signals and optical phenomena in both spatial and frequency domains.
6. Use Taylor and Maclaurin series to approximate functions and evaluate mathematical expressions.
7. Recognize and use selected special functions used in optics.

8. Choose suitable mathematical methods to solve selected problems in the field of optics and interpret the results obtained.

Programme N-PMO-P: Precise Mechanics and Optics, Master's, compulsory-optional

26 hours, compulsory

The exercises focus on practical practice and the application of mathematical methods discussed in the lectures. The student solves selected mathematical and physical problems, which develop their ability to independently choose appropriate mathematical procedures and interpret the obtained results.

Topics of the exercises:

1. Vector spaces, bases, dimensions, and operations with vectors.


2. Complex numbers, complex functions, and their properties.


3. Matrix algebra and its applications.


4. Derivatives of functions and their use in problem-solving.


5. Partial derivatives and differential operators.


6. Indefinite integrals.


7. Definite integrals and the use of integral tables.


8. Double integrals and physical applications.


9. Fourier transform and solving problems in wave optics.


10. Function approximation using Taylor and Maclaurin series.


11. Elementary and special functions used in optics.


12. Comprehensive applied problems linking mathematical methods with optics issues.


13. Classified credit