Mathematics of Continuous World

The course cannot be taken simultaneously with:

Mathematics Analyze (A7B01MAA)
Mathematics of Continuous World (A7B33MSS)

The course is a substitute for:

Mathematics Analyze (A7B01MAA)
Mathematics of Continuous World (A7B33MSS)

Lecturer:

Tutor:

Supervisor:

Department of Cybernetics

Synopsis:

The course is aimed for students of Software Technology and Management

as a substitute of a course of Advanced Calculus in other programmes.

It deals with optimization and calculus of functions of more variables with the use of computer algebra.

Requirements:

Y01MA1

Syllabus of lectures:

1. Distances in multidimensional space (metric, norm).

2. Continuity of functions of more variables.

3. Derivatives of functions of more variables (partial, directional, gradient).

4. Differential of functions of more variables, linear approximation.

5. Derivatives of higher order. Numerical differentiation.

6. Linearity of operators, superposition principle. Line integrals, potential.

7. Multiple integrals.

8. Applications of line integrals. Numerical integration.

9. Differential equations, solvability.

10. Linear differential equations. Numerical solution of differential equations.

11. Fourier series.

12. Approximation of continuous periodic functions.

13. Fourier transform.

Syllabus of tutorials:

1. System Maple

2. Individual work with Maple

3. Derivatives of functions of more variables (partial, directional, gradient).

4. Individual work on assessment tasks

5. Individual work on assessment tasks

6. Line integrals

7. Multiple integrals, relation to derivatives

8. Individual work on assessment tasks

9. Solution of differential equations

10. Individual work on assessment tasks

11. Fourier series

12. Individual work on assessment tasks

13. Fourier transform

Study Objective:

Understanding of basic principles of multivariate calculus, differential equations, Fourier series and Fourier transform.

Study materials:

Ayres, F., Mendelson, E.: Schaum's Outline of Calculus. Edition 4, McGraw-Hill, 1999, ISBN 0070419736.

Bronson, R.: Schaum's Outline of Differential Equations. 2nd edition, McGraw-Hill, 1994, ISBN 0070080194.

Knuth, D.E.: The Art of Computer Programming. Addison Wesley, Boston, 1997.

Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes (The Art of Scientific Computing). Cambridge University Press, Cambridge, 1986.

Wrede, R.C., Spiegel, M.R.: Schaum's Outline of Advanced Calculus. 2nd edition, Mc-Graw-Hill, 2002, ISBN 0071375678.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Inteligentní systémy (compulsory course)