During the lecture of today …
During the lecture of today the following program has been done:
- Derivation of the Heat Equation from basic physical concepts. For this see the file (heat equation.pdf) on my web page.
- Solution of the heat equation with the separation of variables method for both the Dirichlet and Neumann boundary conditions. For this see the file (heat equation.pdf) on my web page plus section 3.1, 3.2, 3.3, 3.5 and 3.6 (up to 3.6.2) from the text book.
Next Lecture on Friday, between 14:15 and 16 at the usual room. Chapter 3 will be finished with the explicit calculation of the Fourier coefficients going through the eigenvalue/eigenfunction problem (section 2.4, 3.4 and 3.6.3). We will also try to start chapter 4 introducing the Fourier discrete analysis of the heat equation.
For next Monday work on exercises: 3.1, 3.2, 3.4, 3.5, 3.8, 3.9, 3.12, 3.13. For some of these you need to know how to calculate explicitly the Fourier coefficients, argument that will be seen next Friday.