Lecture plan/topics

This plan will be updated throughout the semester. Chapters refer to the book by Borthwick.

If you spot any mistakes in some of the notes below, please let me know, so that I can correct them.

Day	Topic	Chapter	Repetition	Assumed knowledge from other courses
18.8	Introduction (selv study)	1	Repetition
	ODE theory and needed notation	2.5-2.6
	Method of characteristics	3.2
19.8	Method of characteristics	3.2-3.4, Notes H,Notes K	Repetition
25.8	Wave equation	4.1-4.4	Repetition	Even and odd extensions of functions
26.8	Wave equation	4.1-4.4	Repetition
1.9	Wave equation	4.6	Repetition
	Vector calculus	2.6
2.9	Wave equation	4.6-4.7	Repetition
8.9	Wave equation	4.6-4.7	Repetition
	Heat equation	6.1-6.4		6.1: selv study
9.9	Heat equation	6.4, Notes H	Repetition
15.9	Heat equation	6.4, Notes H	Repetition
16.9	Heat equation	6.4, Notes H	Repetition
	Laplace equation	9.2, Notes H
22.9	Laplace equation	9.2, Notes H	Repetition
	\(L^p\) spaces	7.1-7.4, Notes K		7.1: inner product spaces, normed vector spaces
23.9	\(L^p\) spaces	7.1-7.4, Notes K	Repetition
29.9	\(L^p\) spaces	7.1-7.4, Notes K	Repetition
	Weak derivatives	10.1
30.9	Conservation laws	10.2, Notes K	Repetition	Green's theorem
6.10	Conservation laws	10.2, Notes K	Repetition
	Sobolev spaces	10.3-10.4
7.10	Weak solutions	10.5-10.6	Repetition
13.10	Poisson equation	11.1-11.3, 11.8	Repetition	11.8: selv study
14.10	Poisson equation	11.1-11.3, 11.8	Repetition
20.10	Poisson equation	11.4	Repetition
	Dirichlet eigenvalues	11.5-11.7		Eigenvalues and eigenvectors
21.10	Dirichlet eigenvalues	11.5-11.7	Repetition	Orthonormal basis, properties of Hilbert spaces
27.10	Dirichlet eigenvalues	11.5-11.7
	Distributions	12.1-3, Notes K	Repetition	There are several common notations for distributions: \(u(\phi)\), \(\langle u,\phi\rangle\), and \((u,\phi)\).
28.10	Distributions	12.1-3, Notes K	Repetition
3.11	Distributions	12.1-3, Notes K	Repetition
	Fundamental solutions	12.4
4.11	Fundamental solutions	12.4	Repetition
10.11	Green's functions	12.5
11.11	Classification of linear PDEs	Chapter 4.4		You must be inside the NTNU network, to have access.
17.11	???
18.11	???