- 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 mathematical 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 focus mainly on the Finite difference methods for solving PDEs and combine learning about their mathematical aspects, such as accuracy and stability, with their practical implementation using Python.
Basic knowledge of Multivariable calculus and Ordinary Differential Equations (ODEs). Knowledge of Numerical methods for ODEs is useful. No previous knowledge of PDEs is required.
Exam, which carries 80% of the final grade and will be written or oral depending on the number of participants, and a coding project, which carries 20% of the final grade.