This course provides a comprehensive introduction to numerical methods for solving mathematical problems commonly encountered in engineering and scientific disciplines. It begins with an overview of fundamental concepts before delving into topics such as solving nonlinear algebraic equations, interpolation, regression, numerical differentiation, and numerical integration. Students will also explore numerical solutions for ordinary differential equations and an introduction to partial differential equations. Throughout the course, we will utilize Python and various scientific packages, including NumPy, SciPy, and Matplotlib, to implement and visualize these numerical methods, ensuring students gain practical computational skills for analyzing and solving complex problems.
| # | Topic | Reading (Reference: Chapter) |
|---|---|---|
| 1 | Introduction | (Dechaumpwhai, 2020): 1; (Kreyszig et al., 2011): 19.1 |
| 2 | Numerical Solution of Nonlinear Algebraic Equations | (Dechaumpwhai, 2020): 2; (Kreyszig et al., 2011): 19.2 |
| 3 | System of Linear Equations | (Dechaumpwhai, 2020): 3; (Kreyszig et al., 2011): 20.1 |
| 4 | Interpolation and Regression | (Dechaumpwhai, 2020): 4; (Kreyszig et al., 2011): 19.3-4 |
| 5 | Interpolation and Regression | |
| 6 | Interpolation and Regression | (Dechaumpwhai, 2020): 5; (Kreyszig et al., 2011): 20.5 |
| 7 | Numerical Differentiation | (Dechaumpwhai, 2020): 6; (Kreyszig et al., 2011): 19.5 |
| 8 | Numerical Differentiation | |
| 9 | Numerical Integration | (Dechaumpwhai, 2020): 6; (Kreyszig et al., 2011): 19.5 |
| 10 | Numerical Integration | |
| 11 | Numerical Integration | |
| 12 | Numerical Solution of Ordinary Differential Equations | (Dechaumpwhai, 2020): 7; (Kreyszig et al., 2011): 21.1-3 |
| 13 | Numerical Solution of Ordinary Differential Equations | |
| 14 | Partial Differential Equations | (Dechaumpwhai, 2020): 7; (Kreyszig et al., 2011): 21.1-4 |