Numerical Mathematics
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Course informations
| Study program level |
Undergraduate |
| Study program |
Computer Science |
| Study program direction |
Software Engineering |
| Course year |
1. |
| Course semester |
II |
| Course status |
Core |
| ECTS |
6 |
| Lectures (h) |
30 |
| Excercises (h) |
30 |
| Seminars (h) |
- |
Course objectives
Acquiring knowledge and skills required for independent work and successful continuation of education. Getting acquainted with the basic ideas and methods of numerical mathematics. In doing so, theorem proof will be avoided, except in the cases of constructive evidence that in itself suggests the construction of ideas or methods. Analyzing the real problem and creating an appropriate numerical mathematical model and critical review of the obtained results.
Course outcomes
- Define the basic ideas and methods of numerical mathematics.
- Apply methods for solving interpolation problems and basic methods for solving linear equation systems.
- Apply methods for solving nonlinear equations and solving nonlinear equations systems.
- Review the approximations of the function, especially in the case of discrete (through the smallest squares problem) and in the case of continuous function (especially Fourier, Chebyshev and some other orthogonal polynomials).
- Apply numerical integration methods.
- Solving simpler problems by applying the learned methods.
Course content
Introduction. Error analysis. Significant digits. A floating point arithmetic. Errors in calculating the function value. Inverse problem in error theory. Interpolation. Spline interpolation. Interpolation problem. Lagrange's form of interpolation polynomial. Newton's form of interpolation polynomial. Error rating. Linear interpolation splines. Cubic interpolation splines. Solving system of linear equations: Solving triangular systems. Gaussian elimination method. LU decomposition. Cholesky-decomposition. QR decomposition. Iterative methods. Decomposition to singular values. Decomposition of eigenvalues. Solving nonlinear equations. Bisection method. The method of simple iterations. Newton's method and modification. Solving the System of Nonlinear Equations: Newton's Method, quasi Newton's Method. Approximation of functions. The best L_2 approximation. Orthogonal polynomials. Chebyshev’s polynomials. Linear and nonlinear problems of the smallest squares.
