# Subject description - AE2B99MAA

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 AE2B99MAA Mathematical Applications Extent of teaching: 2+2c Guarantors: Roles: P,V Language ofteaching: EN Teachers: Completion: KZ Responsible Department: 13131 Credits: 4 Semester: L

Anotation:

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.

Study targets:

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/

Course outlines:

 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

Exercises outline:

 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.

Literature:

 [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.

Requirements:

Basic knowledge of mathematical analysis and linear algebra.

Webpage:

https://moodle.fel.cvut.cz/courses/AE2B99MAA

Subject is included into these academic programs:

 Program Branch Role Recommended semester BEEEM1 Applied Electrical Engineering V 2 BEEEM_BO Common courses V 2 BEEEM2 Electrical Engineering and Management V 2 BEKME1 Communication Technology P 2 BEKME5 Komunikace a elektronika P 2 BEKME_BO Common courses P 2 BEKME4 Network and Information Technology P 2 BEKME3 Applied Electronics P 2 BEKME2 Multimedia Technology P 2 BEKYR1 Robotics V 2 BEKYR_BO Common courses V 2 BEKYR3 Systems and Control V 2 BEKYR2 Sensors and Instrumentation V 2 BEOI1 Computer Systems V 2 BEOI_BO Common courses V 2 BEOI3 Software Systems V 2 BEOI2 Computer and Information Science V 2

 Page updated 20.6.2019 15:53:00, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)