"This course will focus on scientific computation methods for solving initial- and boundary-value problems for partial differential equations, with an emphasis on Finite Difference Methods and Finite Element Methods. Students will have the opportunity to improve their understanding of these methods through programming exercises and the use of simulation software with MATLAB and Python. Some class time will be dedicated to these hands-on activities. This course includes § Finite Difference Approximation for Initial Boundary-Value Problems, Stability of Finite Difference Approximations, Finite Difference Methods in Two Space, Limitations of Finite Difference Approximation, Algorithm Programming and Implementation (with MATLAB or Python). § Galerkin Method: Galerkin Finite Element Method for First and second-Order Equations, Finite-Difference Interpretation of the Galerkin Approximation, Galerkin Finite Element Approximations in Time, Algorithm Programming and Implementation (with MATLAB or Python) § Collocation Method: Collocation Method for First-Order Equations, Collocation Method for Second-Order Equations, Algorithm Programming and Implementation (with MATLAB or Python) § Finite Element Methods in Two Space: Finite Element Approximations over Rectangles, Finite Element A pproximations over Triangles, Algorithm Programming and Implementation (with MATLAB or Python)"