Applied Numerical Mathematics

Lecturer:

Tutor:

Supervisor:

Department of Computer Science and Engineering

Synopsis:

This course is oriented towards practical applications of selected numerical methods demonstrated by examples. It helps to familiarize with basic numerical methods for the evaluation of functions, interpolation, extrapolation, computing of derivation and definite integral, solution of systems of linear algebraic equations, computing non-linear equations and their systems, and numerical data modeling. The next topics of the lectures are: errors, accuracy and stability of numerical computing and related error-free algorithms. Some cryptographic algorithms are also introduced.

Requirements:

Final exam grading is in part derived from the quality of presented homework and activity at seminars.

Syllabus of lectures:

1. Numerical computing in practice

2. Errors, accuracy, and stability of numerical computing

3. Data acquisition and statistical description of data

4. Evaluation of functions

5. Interpolation and extrapolation

6. Computing of derivation and definite integral

7. Solution of systems of linear algebraic equations

8. Computing non-linear equations

9. Solution of non-linear systems of equations

10. Modeling of data

11. Error-free computation

12. Modular arithmetic and error-free algorithms

13. Cryptographic algorithms

14. Random numbers

Syllabus of tutorials:

1. Computing errors and floating point arithmetic

2. Stability of numerical computation

3. Pathological effects in numerical mathematics

4. Evaluation of functions

5. Interpolation and extrapolation

6. Computing of derivation and definite integral

7. Elimination methods of solution of linear algebraic equations

8. Iterative methods of solution of linear algebraic equations

9. Solution of non-linear systems of equations

10. Modeling of data parameters estimation

11. Error-free computation of functions

12. Error-free computation of systems of linear algebraic equations

13. Cryptographic algorithms

14. Monte Carlo methods

Study Objective:

Study materials:

1. Lecture notes (in preparation)

2. http://www.ulib.org/webRoot/Books/Numerical_Recipes/

3. Gregory, R. T. - Krishnamurthy, E. V.: Methods and Applications of Error-free Computation, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo 1994

4. James, V. B. - Kenneth, J. A.: Parameter Estimation in Engineering and Science, John Wiley & Sons, New York, London, Sydney, Toronto 1977

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Computer Technology - Software Engineering- structured studies (compulsory elective course)
• Computer Technology - System Programming- structured studies (compulsory elective course)
• Computer Technology - Computer Graphics- structured studies (compulsory elective course)
• Computer Technology - Computer Network and Internet- structured studies (compulsory elective course)
• Computer Technology - Designing Digital Systems- structured studies (compulsory elective course)