- The student has an overview of a range of techniques to obtain approximate solutions of partial differential equations when analytic methods cannot be applied.
- The student is familiar with the analysis of numerical schemes, considering convergence, accuracy, stability, and relative efficiency.
- The student is familiar with approximation methods for initial-value problems, including single step and multi-step methods.
This numerical analysis course is concerned with the approximate solutions of partial differential equations (PDEs), which are important in quantitative modeling in all fields of science and engineering. In the real world (i.e., outside university), analytic methods can rarely be applied to give quantitative results, so numerical methods are essential. We will combine learning about the mathematical aspects of these numerical methods, such as their accuracy and stability, with the practical implementation.
Analysis 2 (multivariable calculus), basic knowledge of Ordinary Differential Equations (ODEs) and Numerical Methods for ODEs. No previous knowledge of PDEs is required.
Written or oral exam depending on the number of participants. There will be a bonus scheme based on weekly assignments.