Course detail

Selected Parts of Mathematics

FP-VPMAcad. year: 2022/2023

Followed courses Mathematics 1 and Mathematics 2nd The contents are for further study necessary to master the game - approximation of functions with the help of Taylor and Fourier series, other solutions of differential equations and Fourier transform to investigate signals.

Language of instruction

Czech

Mode of study

Not applicable.

Guarantor

Ing. Jiří Kříž, Ph.D.

Department

Institute of Informatics (ÚI)

Learning outcomes of the course unit

The student will be able to analyze the above problem, clarify the appropriate way to address and assess the accuracy of solution due to the specified conditions. Will be able to work with Taylor series and development functions in Taylor series. Become familiar with Fourier series and development functions in Fourier series and the theory of Laplace transform, Fourier and Z-transform.

Prerequisites

Knowledge gained in the course "Mathematics 1", "Mathematics 2" in particular: differential and integral calculus, ordinary differential equations.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The lessons consist of two-hour lecture and two-hour practical seminar. The lecture combines theory with illustrative examples. The practical exercise is concerned on handling numerical tasks.

Assesment methods and criteria linked to learning outcomes

Graded Requirements for credit:
- Active participation in seminars
- Performance of individual tasks
- Semester work with the evaluation of at least E
- Term paper will be delivered by the tutor, the late (unexcused) submission will be penalized by low ratings.

Course curriculum

1. Taylor polynomial, formula, and the rest
2. Taylor series
3. The solution chosen ordinary differential equations and their applications
4. Fourier series
5. Fourier transformation

The exercise will always practice the following week odpřednášená relevant parts, including self-solved problems.

Work placements

Not applicable.

Aims

Complement and deepen the mathematical knowledge of students continuing a Master's degree more directly on the 4th year of the required parts.

Specification of controlled education, way of implementation and compensation for absences

Attendance at lectures is not checked. Attendance at seminars is systematically checked. Apologies absence accepts and acknowledges the instructor.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

studentům bude předán přehled pro praxi vhodných podkladů z různých zdrojů a později specializovaný učební text (CS)

Recommended reading

studentům bude předán přehled pro praxi vhodných podkladů z různých zdrojů a později specializovaný učební text (CS)

Classification of course in study plans

  • Programme BAK-MIn-D Bachelor's

    branch BAK-MIn , 3 year of study, summer semester, elective

Type of course unit

 

Lecture

10 hod., optionally

Teacher / Lecturer

Ing. Jiří Kříž, Ph.D.

Syllabus

1. Repetition (needed lots of Mathematics 1, Mathematics 2, infinite series, power series)
2. Taylor polynomial, formula, rest, Taylor series and their use
3. Fourier series, Fourier transform and its use
4. Laplace transform and its use
5. Z-transform and its use

Exercise

10 hod., compulsory

Teacher / Lecturer

Ing. Jiří Kříž, Ph.D.

Syllabus

The exercise will always practice the following week odpřednášená relevant parts, including self-solved problems.