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The course is introductory to scientific computation. The basic numerical methods for the solution of classical problems are presented and described. The course is introductory to scientific computation. The basic numerical methods for the solution of classical problems are presented and described. |
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Basic linear algebra and computer programming. |
- Basic concepts of floating-point arithmetic. Conditioning of a problem. Numerical stability of an algorithm.
- Linear systems: direct methods (Gaussian eliminitations, LU-decomposition, Choleski) and iterative methods (Jacobi, Gauss-Seidel, SOR).
- Approximation of functions and data: polynomial and piecewise polynomial interpolation, splines, discrete least squares.
- Non-linear equations and systems: Newton's method and its discrete variants, fixed-point iteration.
- Numerical integration: Newton-Cotes formulas, Gaussian quadrature rules, composite rules.
- Initial value problems for ordinary differential equations: one-step methods (Runge-Kutta methods) and multistep (Adams) methods. Stiff problems.
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