### DisCont mathematics 2

#### Course Description

#### General Competencies

Learning advanced and modern techniques of evaluation of the values of some functions and various forms of its approximations.

#### Learning Outcomes

- Understand the principles of numerical calculation of some elementary functions.
- Understand the principles of varyous types of approximations.
- Use the technique of approximatrion of a function by orthogonal polynomials.
- Use the technique of fast summing algorithms.
- Use the technique of acceleration of the convergence of some numerical series.
- Understzand the asymptotical convergence and its application in calculations of values of some special functions.
- Learn how to use modern mathematical literature
- Lear how to use mathematical software in solving of complex problems.

#### Forms of Teaching

**Lectures**Lectures are organized through two cycles. The first cycle consists of 7 weeks of classes and mid-term exam, a second cycle of 6 weeks of classes and final exam. Classes are conducted through a total of 15 weeks with a weekly load of 4 hours.

**Exams**Mid-term exam in the 8th week of classes and final exam in the 15th week of classes.

**Consultations**Consultations are held one hour weekly according to arrangement with students.

**Other**Student's seminars.

#### Grading Method

Continuous Assessment | Exam | |||||
---|---|---|---|---|---|---|

Type | Threshold | Percent of Grade | Comment: | Percent of Grade | ||

Homeworks | 0 % | 20 % | 0 % | 20 % | ||

Seminar/Project | 0 % | 10 % | 0 % | 10 % | ||

Mid Term Exam: Written | 0 % | 30 % | 0 % | |||

Final Exam: Written | 0 % | 40 % | ||||

Exam: Written | 0 % | 60 % |

#### Week by Week Schedule

- Evaluation of values of functions. Horner's algorithm. Fast summation algorithm. identities.
- Solving algebraic equations
- Acceleration of convergence. Manipulation with series.
- The connection between integrals and sums. Complex techniques of summing.
- Continued fractions. Basic properties and formulas.
- Representation of numbers and functions by continued fractions. Rational approximations.
- Orthogonal polynomials. Polynomials given by reccursive relations. Applications of fast summing algorithms
- Exam
- Čebyšev's polynomials and problem of approximations. Fast calculations of Fourier series.
- Series of functions. Generating functions of functional series. Z-transformation
- Factorial and gamma functions. Stirling formula. Approximations of binomial coefficients.
- Asympthotic behaviour. Asymptotic series.
- Harmonic series and related problems. Euler constant.
- Student seminar. Solution of advanced problems
- Exam

#### Study Programmes

Electrical Engineering and Information Technology -> Electrical Engineering and Information Technology and Computing (Study)

Computing -> Electrical Engineering and Information Technology and Computing (Study)

Control Engineering and Automation -> Electrical Engineering and Information Technology (Module)

Electrical Power Engineering -> Electrical Engineering and Information Technology (Module)

Electronic and Computer Engineering -> Electrical Engineering and Information Technology (Module)

Electronics -> Electrical Engineering and Information Technology (Module)

Wireless Technologies -> Electrical Engineering and Information Technology (Module)

Information Processing -> Computing (Module)

Software Engineering and Information Systems -> Computing (Module)

Computer Engineering -> Computing (Module)

Computer Science -> Computing (Module)

Telecommunication and Informatics -> Computing (Module)

#### Prerequisites

#### Literature

*Numerical Methods That Usually Work*, Mathematical Association of America

*Experimentation in Mathematics, Computational Paths to Discovery*, A. K. Peters

*Companion to Concrete Mathematics, Mathematical Techniques and Various Applications*, John Wiley & Sons

*Handbook of Continued Fractions for Special Functions*, Springer

*Irresistible Integrals - Symbolics, Analysis and Experiments in the Evaluation of Integrals*, Cambridge University Press

#### Lecturers in Charge

#### Grading System

**6**ECTS

**L0**English Level

**L1**e-Learning

**60**Lecturers

**0**Exercises

**0**Laboratory exercises

#### Grading

**80**Excellent

**70**Very Good

**60**Good

**50**Acceptable