### DisCont mathematics 2

#### Course Description

Selected topics of discrete mathematics and mathematical analysis, with emphasis on solving complex examples and tasks, based on algorithmic approach.

#### 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 | Threshold | 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

##### University undergraduate

[FER2-HR] Computer Engineering - module

Courses for exceptionally successful students
(5. semester)
[FER2-HR] Computer Science - module

Courses for exceptionally successful students
(5. semester)
[FER2-HR] Computing - study

Courses for exceptionally successful students
(3. semester)
[FER2-HR] Control Engineering and Automation - module

Courses for exceptionally successful students
(5. semester)
[FER2-HR] Electrical Engineering and Information Technology - study

Courses for exceptionally successful students
(3. semester)
[FER2-HR] Electrical Power Engineering - module

Courses for exceptionally successful students
(5. semester)
[FER2-HR] Electronic and Computer Engineering - module

Courses for exceptionally successful students
(5. semester)
[FER2-HR] Electronics - module

Courses for exceptionally successful students
(5. semester)
[FER2-HR] Information Processing - module

Courses for exceptionally successful students
(5. semester)
[FER2-HR] Software Engineering and Information Systems - module

Courses for exceptionally successful students
(5. semester)
[FER2-HR] Telecommunication and Informatics - module

Courses for exceptionally successful students
(5. semester)
[FER2-HR] Wireless Technologies - module

Courses for exceptionally successful students
(5. semester)
#### Literature

F. S. Acton (1990.),

*Numerical Methods That Usually Work*, Mathematical Association of America
J. Borwein J, D. Bailey, R. Girgensohn (2004.),

*Experimentation in Mathematics, Computational Paths to Discovery*, A. K. Peters
Z. A. Melzak (1973.),

*Companion to Concrete Mathematics, Mathematical Techniques and Various Applications*, John Wiley & Sons
A. Cuyt et al (2008.),

*Handbook of Continued Fractions for Special Functions*, Springer
G. Boros, V. Moll (2004.),

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

#### For students

#### General

**ID**90095

Winter semester

**6**ECTS

**L0**English Level

**L1**e-Learning

**60**Lectures

**0**Seminar

**0**Exercises

**0**Laboratory exercises

**0**Project laboratory

#### Grading System

**80**Excellent

**70**Very Good

**60**Good

**50**Sufficient