Mathematical Applications
Code  Completion  Credits  Range  Language 

AE2B99MAA  KZ  4  2+2c 
 Prerequisite:
 Linear Algebra and its Applications (AE0B01LAA)
Introduction to Calculus (AE0B01MA1)  Lecturer:
 Tutor:
 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 mfiles 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., SpringerVerlag, 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, SpringerVerlag, 1993.
[6] Etter,D.M.: Engineering Problem Solving with MATLAB (2nd Edition), Prentice Hall,1996.
 Note:
 Further information:
 https://moodle.fel.cvut.cz/courses/AE2B99MAA
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Cybernetics and Robotics  Robotics (elective course)
 Cybernetics and Robotics  Senzors and Instrumention (elective course)
 Cybernetics and Robotics  Systems and Control (elective course)
 Electrical Engineering, Power Engineering and Management  Applied Electrical Engineering (elective course)
 Electrical Engineering, Power Engineering and Management  Electrical Engineering and Management (elective course)
 Communications, Multimedia and Electronics  Communication Technology (compulsory course in the program)
 Communications, Multimedia and Electronics  Multimedia Technology (compulsory course in the program)
 Communications, Multimedia and Electronics  Applied Electronics (compulsory course in the program)
 Communications, Multimedia and Electronics  Network and Information Technology (compulsory course in the program)
 Open Informatics  Computer Systems (elective course)
 Open Informatics  Computer and Information Science (elective course)
 Open Informatics  Software Systems (elective course)
 Electrical Engineering, Power Engineering and Management (elective course)
 Communications, Multimedia and Electronics (compulsory course in the program)
 Cybernetics and Robotics (elective course)
 Open Informatics (elective course)
 Communications, Multimedia and Electronics  Communications and Electronics (compulsory course in the program)