Mathematical Applications

Prerequisite:

Linear Algebra and its Applications (AD0B01LAA)
Introduction to Calculus (AD0B01MA1)

Lecturer:

Jan Bičák, Roman Čmejla

Tutor:

Jan Bičák, Roman Čmejla

Supervisor:

Department of Circuit Theory

Synopsis:

The course is designed to acquaint students with the basics work in the mathematical programs Maple and MATLAB. The first part of the course is devoted to the algebraic system Maple and its use for for solving differential and integral calculus of one variable, linear algebra and arithmetic with complex numbers. The second part of the subject is devoted to MatLab program and its application in solving computational problems in engineering practice, particularly for signal processing. Next, there is an introduction to the analysis of electrical circuits in the program Maple with PraCAn package.

Requirements:

Basic knowledge of mathematical analysis and linear algebra.

Syllabus of lectures:

1. Programs for solving mathematical problems, introducing to Maple worksheet, basic Maple commands, handling with numbers, term and function definition.

2. Introduction to Maple: solving equation, function plotting, basic programming.

3. Using Maple in the differential and integral calculus of functions of one variable.

4. Using Maple in linear algebra - matrix algebra, solving systems of linear equations.

5. Using Maple for the functions of complex variables - complex numbers, elementary functions and multivalued.

6. Introduction to MATLAB; help, matrices, vectors, scalars, indexing matrices and

vectors, basic operations, complex numbers.

7. Graphical representation of data in MATLAB; tools for plotting, printing and exporting

graphics, 3D Graphics, data import and export.

8. Signals with MATLAB; convolution, correlation, filtering, spectral analysis.

9. Scripts and Functions in MATLAB; program flow, user defined functions.

10. Electromagnetics with MATLAB; electrostatic and magnetostatic fields, wave propagation,

transmission lines (transient effects, pulse propagation, lossy transmission lines).

11. Developing of user applications.

12. PraCAn package - the possibility of electrical circuits analysis in Maple.

13. Reserve

Syllabus of tutorials:

1. Environment of Maple program (Maple Classic Worksheet, Maple Standard Worksheet), elementary calculations.

2. Polynomials, rational functions, the roots of polynomial and equations system, plotting of functions, solving of individual tasks using Maple.

3. Solution of differential and integral calculus of one variable.

4. TEST. Solution of linear algebra.

5. Functions of complex variables - basic arithmetic operations and standard functions, examples.

6. TEST.

7. Matlab command line; basic operation, sinusoidal signal generation. TEST.

8. Data import and export, plotting, sounding.

9. Signal filtering and plotting in frequency domain. TEST.

10. Writing scripts and m-files for signal processing in time domain.

11. Visualization of wave propagation along transmission line. TEST.

12. Virtual piano design.

13. Analysis of electric circuits by PraCAn package - solving of resistance circuits, harmonic steady state and transient analysis.

14. TEST. Credits.

Study Objective:

The course is designed to acquaint students with the basics work in the mathematical programs Maple and MATLAB for mathematical problems in technical branches.

Classification: knowledge are tested on selected exercises. The total score of the tests determines the grade.

More info: https://moodle.kme.fel.cvut.cz/

Study materials:

[1] Heck, A.: Introduction to Maple, 2nd ed., Springer-Verlag, Berlin, 1996

[2] Maple Getting Started Guide, Waterloo Maple Inc.

[3] Char, B.W.: Maple Learning Guide, Waterloo Maple Inc.

[4] Monagan, M.B., Geddes, K.O., a kol.: Maple Inroductory Programming Guide, Waterloo Maple Inc.

[5] , S.Lang: Complex Analysis, Springer-Verlag, 1993.

[6] Etter,D.M.: Engineering Problem Solving with MATLAB (2nd Edition), Prentice Hall,1996.

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• Komunikace, multimedia a elektronika - Komunikační technika_163439 (compulsory course in the program)
• Komunikace, multimedia a elektronika - Multimediální technika_163458 (compulsory course in the program)
• Komunikace, multimedia a elektronika - Aplikovaná elektronika_163524 (compulsory course in the program)
• Komunikace, multimedia a elektronika - Síťové a informační technologie_163540 (compulsory course in the program)
• Komunikace, multimedia a elektronika, před rozřazením do oborů (compulsory course in the program)
• Komunikace, multimédia a elektronika (compulsory course in the program)