Description
This course covers Laplace transform for ordinary differential equations, Sturm-Liouville theory, Fourier series, partial differential equations and Fourier transform.
Textbook: Differential Equations with Boundary-Value Problems, by D. G. Zill, Cengage, 9th edition.
Content
| section | topic |
|---|---|
| 7.1 | Definition of the Laplace transform |
| 7.2.1 | Inverse transforms + Intro to Mathematica |
| 7.2.2 | Transforms of derivatives |
| 7.3.1 | Translation on the s-axis |
| 7.3.2 | Translation on the t-axis |
| 7.4.1 | Derivatives of transforms |
| 7.4.2 | The convolution theorem |
| 7.4.3 | Transforms of periodic functions |
| 7.5 | The Dirac delta function |
| 7.6 | Systems of linear differential equations |
| 11.1 | Orthogonal functions |
| 11.2 | Fourier series |
| 11.3 | Fourier cosine and sine series |
| 11.4 | Sturm-Liouville Problems |
| 11.4 | Sturm-Liouville Problems |
| 12.1 | Separable PDEs |
| 12.2 | Boundary value problems |
| 12.3 | The heat equation |
| 12.4 | The wave equation |
| 12.5 | Laplace equation |
| 12.5 | Laplace equation |
| 12.6 | Non-Homogeneous PDEs |
| 12.8 | Higher dimensional problems |
| 13.1 | Laplace equation in polar coordinates |
| 14.2 | Laplace transform for the heat equation |
| 14.3 | Fourier integral |
| 14.4 | Fourier transform for PDEs |
Resources
🚧 In the future, I will add a link to my lecture notes here.