Mathematics 2 for Audio Engineering
FEKT-JMA2Acad. year: 2017/2018
Calculus of the more variable functions.
Ordinary differential equations - basic terms, exact methods for differential equations of first order, linear differential equations and its applications.
Complex functions - basic notions, differential and integral calculus, Cauchy theorem, Laurent's series, residue theorem.
Fourier series and Fourier transform, Laplace transform, and its applications in electrotechnics. Z transform and application of its to difference equations. Introduce to numerical methods.
Basics of probability theory, random variable, law of large numbers. Introduce to mathematical statistics.
Learning outcomes of the course unit
After the graduation of the course the students should be able
- use some analytical and numerical methods to solve differential equations
-expain the basic notions and methods of differential and integral calculus of complex functions
- use Laplace and Fourier transformation for solving differential and integral equations in physics and engineering
- use Z- transformation for solving discrete equations
- define the basic principles of numerical analysis
- use the methods of probability and statistics in concrete problems.
The subject knowledge on the secondary school level course is requested. Explain the basic principles and methods of linear algebra, differential and integral calculus.
Recommended optional programme components
Recommended or required reading
Hlávka J., Klátil J., Kubík S.: Komplexní proměnná v elektrotechnice. SNTL Praha 1990. (CS)
Škrášek J., Tichý Z.: Základy aplikované matematiky II. SNTL Praha 1983. (CS)
Aramanovič, I.G., Lunc, G. L., Elsgolc, L.E.: Funkcie komplexnej premennej, Operátorový počet, Teória stability (CS)
Kolářová, E.:MATEMATIKA 2 Sbírka úloh (CS)
Chvalina, J., Svoboda, Z., Novák,M.: Matematika 2 (CS)
Melkes, F., Řezáč, M.: Matematika 2(BMA2 et KMA2) (CS)
FAJMON, B., RŮŽIČKOVÁ, I. MATEMATIKA_3_S.PDF. Matematika 3. Brno: UMAT FEKT VUT, 2003. s. 1-266. (CS)
Hlavičková, I., Hliněná, D.: Matematika 3 - sbírka úloh z pravděpodobnosti (CS)
Planned learning activities and teaching methods
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.
Assesment methods and criteria linked to learning outcomes
The course is evaluated by maximum 100 points such that
up to 30 points from computer exercises and the other activities (2 projects and 2 written tests)
up to 70 points from examination paper.
For course-unit credit 10 points from the student's work during the semestr is required
Language of instruction
1. Calculus of the more variable functions.
2. Ordinary differential equations, basic terms, exact methods for the equation of the 1. order
3. Linear differential equations.
4. Complex functions - basic terms and differential calculus.
5. Basic of integral calculus, Cauchy theorem.
6. Laurent's series, residue theorem.
7. Fourier series and Fourier transform.
8. Laplace transform, and its usage.
9. Z transform and application of its to difference equations .
10. Basic of numerical analysis and methods,.
11. Basic of probability.
12. Random variable.
13. Law of large numbers and basic of mathematical statistics.
Knowledge of fundamental methods for solving the ordinary differential equations. To utilize the complex analysis to application of Laplace, Fourier and Z transforms in the first part. Other parts are devoted to introduction into numerical analysis and probability and statistics.
Specification of controlled education, way of implementation and compensation for absences
Computer exercise and the other activities are compulsory. Properly excused absence can be replaced by individual homework.
Specifications of the controlled activities and ways of implementation are provided in annual public notice.