Introduction for the course fall 2013 takes place Wednesday sixth of November 1pm in room B2034.
General remarks. We give two courses on differential equations. First ordinary differential equations (ODE) and then this course on partial differential equations (PDE). For ODE's the unknown function(s) depend on only one variable (usually time) while for PDE's the unknown function depend on two or more variables (space variables or space + time).
Litterature: "Elementary Differential Equations and Boundary Value Problems" by Boyce&DiPrima (John Wiley), 8:th edition or later. The PDE-course covers chapters 5,(10),11. Excellent complements are "Ordinära Differentialekvationer" by Andersson&Böiers (many proofs but in swedish) and "Differential equations with applications and historical notes" by G.F. Simmons (very interesting historical notes). First week we will study first order PDEs and give an introduction to the subject, see lecture 1-3.
Study material.
Lecture 1. First order PDE. Sound to lecture 1
Lecture 2. Overview of PDE's. Sound to lecture 2
Lecture 3. Nodal structure in 2D box. Sound to lecture 3
Lecture 4 Series Solutions Near an Ordinary Point. Sound to lecture 4.
Lecture 5 Regular singular points. Sound to lecture 5.
Lecture 6 Series Solutions Near a Regular Singular Point Sound to lecture 6.
Lecture 7 Inner product and self-adjoint matrices. Sound to lecture 7.
Lecture 8 Boundary Value Problems I Sound to lecture 8.
Lecture 9 Boundary Value Problems II Sound to lecture 9.
Lecture 10 Nonhomogeneous BVP Sound to lecture 10.
Lecture 11 Notes on Green function Sound to lecture 11.
Lecture 12 How to obtain Liouville normal form Sound to lecture 12.
Lecture 13 Singular SL-problems and Bessel's equation Sound to lecture 13.
Lecture 14 Notes on convergence of expansions Sound to lecture 14.
Examination: Individual home exam. Distributed week 50 and solutions presented 9th of January. An example of a home exam from last year. Solutions in LaTeX. Three theoretical questions and two numerical.
Lecture rooms on Wednesdays:
w45: B2034 13-15
w46: B2034 13-15
w48: D1140 13-15
w49: D0073 13-15
w50: D1140 13-15
Plan :
w45: PDE-introduction.First-order PDE. Lecture 1-3.
w46: Series solutions of ODE.Lecture 4-6.
w48: Sturm-Liouville theory I. Lecture 7-10.
w49: Sturm-Liouville theory II. Green function. Lecture 11-14
w50: Repetition.
Exercises in the 8:th edition:
Chapter 5:
1.2, 1.4, 1.9, 1.16, 1.18
2.2, 2.5, 2.14, 2.21
3.2, 3.10, 3.22, 3.27
4.1, 4.3, 4.19, 4.25
5.2, 5.17, 5.23, 5.24, 5.25
6.1, 6.12, 6.13
7.2, 7.5, 7.9, 7.18, 7.19
8.10, 8.12, 8.13, 8.14.
Chapter 11:
1.1, 1.2, 1.3, 1.7, 1.13, 1.16, 1. 17, 1.19, 1.22, 1.23
2.1, 2.4, 2.7, 2.15, 2.16, 2.20, 2.23, 2.25a
3.1, 3.6, 3.17, 3.18, 3.19, 3.28
4.1, 4.3, 4.5
5.1, 5.3, 5.4, 5.5, 5.6, 5.7, 5.9
6.4, 6.6, 6.8.
Mathematica problems
Two examples with regular singular point at x=0
A series solution for -y''=2y+x, y(0)=y(1)=0.
Some links:
Back to Hans Frisk's homepage.
senast uppdaterad den 27/11 2013