Learning Outcomes
1. Have a complete understanding of the advantages, disadvantages and limitations of numerical methods.
2. Have a complete understanding of common numerical methods and how they are used to obtain approximate solutions to otherwise intractable mathematical problems.
3. Apply numerical methods to obtain approximate solutions to mathematical problems.
4. Apply numerical methods for various mathematical operations and tasks, such as interpolation, integration, solution of nonlinear equations, solution of systems of linear equations.
5. Analyse and evaluate the accuracy of common numerical methods.
6. Be aware of the computational tools and the numerical libraries that can be used in order to solve numerical analysis problems.
Course Content (Syllabus)
Errors. Solving nonlinear equations in one variable. Matrices, eigenvalues and eigenvectors. Solving systems of linear equations. Interpolation. Least squares. Householder transformations. QR factorization. Numerical integration. Linear programming methods (and related optimization topics). Solving initial-value problems for ordinary differential equations.
Keywords
Errors, Root finding, Interpolation, Numerical integration, Numerical Linear Algebra, Numerical Solution of Ordinary Differential Equations, Least Squares, Householder Factorization