Computer algebra systems

Lecturer:

Tutor:

Supervisor:

Department of Natural Sciences

Synopsis:

Introduction to computer algebra systems (MAPLE, MATHEMATICA,

MATLAB), history, general properties, comparison. Students are

introduced into symbolic and numerical operations, programming and

debugging, libraries and data structures, solving problems, matrix

operations, logic operations and graphics in each of the systems.

Requirements:

Assessment: active participation in labs, competion of the tasks, (5 tasks, of them 3 solved in MATLAB, 1 in Maple, 1 in Mathematica).

Syllabus of lectures:

1.Mathematical software, overview.

MATLAB: Philosophy of the system, objects, overview.

2.Programming tools,m-scripts and m-functions development.

3.Recursion principle, model examples real world applications.

4.Sparse matrices, operations, solving problems with sparse matrices.

5.Symbolic operations, solution of fundamental mathematical problems.

6.Presentation of model problems solution.

7.Graphical tools. GUI tools, technical applications.

8.Maple: Intro, fundamentals, principles, capabilities.

9.Advantages, disadvanatages, problems.

10.Presentation of model problems solution.

11.Mathematica: Intro, fundamentals, tools, capabilities.

12.Advantages, disadvanatages, problems.

13.Presentation of model problems solution.

14.Dokumentační nástroje matematického SW.

Syllabus of tutorials:

1. Basic informations.

2. System Derive: Introduction.

3. Individual experiments and solution of a project.

4. System Maple: Introduction.

5. Tutorial worksheets.

6. Individual experiments and solution of a project.

7. Individual experiments and solution of a project.

8. Individual experiments and solution of a project.

9. Individual experiments and solution of a project.

10. System Mathematica: Introduction.

11. Individual experiments and solution of a project.

12. Systém MatLab: Introduction.

13. Individual experiments and solution of a project.

14. Committal of a project.

Study Objective:

Gain practical experience in formulating and solving various mathematical problems with the aid of MSW.

Solve and present the solution with the aid of MSW.

Knowledge of the capabilities of the MSW, experince with each of the presented ones should help the students in design, and strategy of engineering problems solution, their diploma thesis, or other subjects, where MSW is an essential support.

Study materials:

[1] Hanselman, D., Littlefield, B.: Mastering MATLAB, Prentice Hall, New Jersey, 2001

[2] Ch. Van Loan: Computing with MATLAB, 2004

[3] F.C.Hoppensteadt, Ch.S.Peskin: Modeling and Simulation in Medicine and the Life

Sciences, 2e., Springer, 2002

[4] D.J. Higham, N.J. Higham: MATLAB Guide, SIAM, Philadelphia, 2000

[5] Introduction to Derive 6, Chapters 1 & 2, Texas Instruments,Dallas, 2003

[6] Maple 9.5 Getting Started Guide, Waterloo Maple Inc., 2003

[7] Char, B.W.: Maple 9 Learning Guide, Waterloo Maple Inc., 2003

[8] Wolfram, S.: The Mathematica Book, Fourth Ed., Cambridge University Press, 1999

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Navazující magisterský studijní obor Přístroje a metody pro biomedicínu - prezenční v angličtině (compulsory elective course)