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 us know, so that we can correct them.

Day	Topic	Chapter	Repetition	Assumed knowledge from other courses
22.8.23	Introduction (selv study)	1	Repetition
	ODE theory and needed notation	2.5-2.6
	Method of characteristics	3.2
25.8.23	Method of characteristics	3.2-3.4, Notes H,Notes K	Repetition
29.8.23	Method of characteristics	3.2-3.4, Notes H, Notes K	Repetition
	Wave equation	4.1-4.4		Even and odd extensions of functions
1.9.23	Wave equation	4.5-4.6	Repetition	Surface integrals (over spheres). Remark: 4.5 not treated in class.
5.9.23	Wave equation	4.6-?	Repetition	double and triple integrals, surface integrals
	Vector calculus	2.6
8.9.23	Wave equation	4.6-4.7	Repetition
12.9.23	Domain of Dependence	(6.1). 6.2-6.3	Repetition	6.1 self study.
	Wave Equation. Heat Equation.
15.9.23	Heat equation. Section 9.5 (or notes).Parabolic. Max.Pr.. One-dim.	6.4, Notes H	Repetition
19.9.23	Heat equation	Notes H 6.4	Repetition
22.9.23	Burgers's Eqn. with viscosity (short remark). The Laplace equation	9.2, Notes H	Repetition
26.9.23	Laplace equation	9.2, Notes H	Repetition
	\(L^p\) spaces	7.1-7.4, Notes K		7.1: inner product space, normed vector spaces
29.9.23	\(L^p\) spaces	7.1-7.4, Notes K	Repetition
3.10.23	\(L^p\) spaces	7.1-7.4, Notes K	Repetition
				The proof of Theorem 12.9 was sketched, page 253.
6.10.23	Conservation laws. Weak derivatives (Sobolev deriv.)	10.1, 10.2Weak Solutions and Shocks	Repetition	Green's theorem
10.10.23	Conservation laws		Repetition
	Sobolev spaces
13.10.23	Weak solutions	Chapter 10	Repetition	Chapter 10. (Section 10.4 without proofs).
17.10.23	Weak solutions		Repetition
	Dirichlet's Problem	11.1 -11.3.	dElementary notes	11.4 without proof.
20.10.23	Poisson equation. Eigenvalues. Variational Principles.	11.3, 11.5. Not regularity issues.	Repetition
Harald Hanche-Olsen lectured the following two weeks (four lectures)
24.10.23	Distributions	12.1-3, Notes K	Repetition	There are several common notations for distributions: \(u(\phi)\), \(\langle u,\phi\rangle\), and \((u,\phi)\).
27.10.23	Distributions	12.1-3, Notes K	Repetition
31.10.23	Fundamental solutions	12.4, Notes H
14.11.23	Classification of 2nd order equarions	12.5, Notes H	F. John. Partial Differential Equations, Ch. 2.1. Springer
17.11.23	Elliptic 2nd order Equations: Maximum Principle.	Section 9.4. See also Weak Maximum Principle
21.11.23 and 24.11.23	Mostly repetiotion and examples.		Repetitio mater studiorum est
			Repetition	Eigenvalues and eigenvectors
10.11.23 and 7.11.23	Calculus of Variations. Dirichlet Eigenvalues.	11.5 and 11.8 11.7		Orthonormal basis, Properties of Hilbert spaces





	Classification of linear PDEs	Chapter 4.4		You must be inside the NTNU network, to have access.
12.12.23	Exam. 2023.			Focus: The problems you are most intersted in.