Numerical Analysis

Grading of the course requires grading of the following courses:

Introduction to Algebra (X01ALG)
Mathematics 1 (X01MA1)
Mathematics 2 (X01MA2)

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course covers numerical methods essential for engineering applications (interpolation and approximation of functions, splines, numerical differentiation and integration, roots of polynomials and other functions, numerical solving of differential equations). Each topic is demonstrated by a program module in Maple and students are required to solve concrete problems.

Requirements:

The first two courses of bachelor studies, mathematics and programming.

Syllabus of lectures:

1. Introductiom to numerical problems.

2. Approximation of functions, polynomial interpolation.

3. Error estimates for polynomial interpolation.

4. Hermite interpolation polynomial. Splines.

5. Least square method.

6. Numerical differentiation. Richardson extrapolation.

7. Numerical integration. Error stimates, choice of integration steps.

8. Gaussian integration, Romberg method.

9. One-step methods of solving differential equations.

10. Other methods of solving differential equations.

11. Basic methods of finding roots of functions.

12. Iterative methods, fixed point theorem.

13. Finding complex roots and solution of systems of nonlinear equations.

14. Roots of polynomials.

Syllabus of tutorials:

1. Introduction to numerical problems.

2. Approximation of functions, polynomial interpolation.

3. Error estimates for polynomial interpolation.

4. Hermite interpolation polynomial. Splines.

5. Least square method.

6. Numerical differentiation. Richardson extrapolation.

7. Numerical integration. Error estimates, choice of integration steps.

8. Gaussian integration, Romberg method.

9. One-step methods of solving differential equations.

10. Other methods of solving differential equations.

11. Basic methods of finding roots of functions.

12. Iterative methods, fixed point theorem.

13. Finding complex roots and solution of systems of nonlinear equations.

14. Roots of polynomials.

Study Objective:

Basic methods of approximation, numerical differentiation and integration, numerical solution to algebraic, transcendent and differential equations.

Study materials:

1. Press, W., Flannery, B., Teukolsky, S.: Numerical Recipes in Pascal: The Art of Scientific Computing, Cambridge Univ. Press, Cambridge, 1986.

2. Redfern, D.: The Maple Handbook, Springer-Verlag, Berlin, 1994.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Computer Technology- structured studies (compulsory elective course)
• Softwarové inženýrství (elective specialized course)
• Web a multimedia (elective specialized course)
• Manažerská informatika (elective specialized course)
• Inteligentní systémy (elective specialized course)