| Area of Mathematics: | Computational and Applied Mathematics |
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| Semester: | 4ο | ||
| Course ID: | 41403 | ||
| Course Type: | Compulsory | ||
| Teaching hours per week: | Theory: 4 | Practice: 0 | Laboratory: 2 |
| ECTS : | 7 | ||
| Eclass: | For the course’s material, click here. | ||
| Instructors: | Aretaki Aikaterini | ||
Description
- Floating point arithmetic. Error estimation, round-off errors and their influence on computations.
- Linear systems: Gauss elimination, LU factorization. Vector and matrix norms. Condition number and linear system sensitivity analysis. Jacobi and Gauss – Seidel iterative methods.
- Interpolation and approximation: Lagrange polynomial interpolation, Newton polynomial with divided differences, Hermite interpolation, linear and cubic splines.
- Numerical integration: Newton-Cotes quadrature methods, mid-point, trapezoidal and Simpson’s rules. Gauss-Legendre quadrature methods.
- Numerical differentiation and finite differences formulations.
- Numerical solution of nonlinear equations: Iteration method, bisection, fixed-point iteration, Newton – Raphson, secant.
- Basic properties of numerical methods for partial differential equations. Euler’s and Runge-Kutta methods on initial value problems for ordinary differential equations.
Bibliography
- Burden R.L., Faires D.F., Numerical Analysis, 5th ed. PWS-Kent, Boston, MA.
- Cheney W., Kincaid D., Numerical Analysis and Computing, 6th ed., Brooks/Cole, Pacific Grove, CA.
- Quarteroni A., Saleri F., Gervasio P., Scientific computing with Matlab and Octave, 3rd ed., Springer, 2014.
