MAT394 Partial Differential Equations (TOC)
Week 1
Introduction
(external link)
First order PDEs
Fully nonlinear first order PDEs
(advanced topic)
Homogeneous 1D wave equation
Extras.
For the 1-st week look at
2011F home assignment 1
(solutions are discussed on
Forum 2011#6.0
)
Home Assignment 1
, deadline: Fri October 4
Week 2
1D Wave equation reloaded: characteristic coordinates
Wave equation reloaded (continued)
1D Wave equation reloaded: discussion and examples
Extras.
For the 1-st week look at
2011F home assignment 2
(solutions are discussed on
Forum 2011#8.0
)
Home Assignment 2
, deadline: Fri October 11
Week 3
1D Wave equation: IBVP
,
1D Wave equation: Misc
, and
Hyperbolic first order systems with one spatial variable
Energy integral
Relax!
Week 4
1D Heat equation: method of self-similar solutions
1D Heat equation: Misc
--Coming
1D Heat equation: Misc. II
--Coming
Extras.
For the 3-rd and 4-th weeks look at
2011F home assignment 3
(solutions are discussed on
Forum 2011#9.0
)
Extras.
1D Diffusion Equation: Introduction
--(external link) Slide presentation, press "Space" or "->" for the next slide and "<-" for the previous one.
Home Assignment 3
, deadline: Fri October 18
Week 5
Separation of variables: 1D wave equation
Eigenvalue problems (examples)
Ortogonal systems
Extras.
Separation of Variables: Introduction
--Slide presentation
Home Assignment 4
, deadline: Fri October 25
Week 6
Ortogonal systems and Fourier series
Other Fourier series
Extras.
Separation of Variables: Introduction
--Slide presentation
Home Assignment 5
.
Week 7
Fourier transform, Fourier integral
Properties of Fourier transform
Applications of Fourier transform to PDEs
Home Assignment 6
.
Week 8
Separation of variables: heat equation
Separation of variables: Misc equations
Laplacian in polar and spherical coordinates
Laplacian: separation of variables in polar coordinates
Home Assignment 7
.
Week 9
Laplacian: separation of variables in polar coordinates. II
General properties of Laplace equation
Potential theory and around
Green function
Home Assignment 8
.
Week 10
Wave equation--solution
Wave equation: energy method
Separation of variables in spherical coordinates
Home Assignment 8
.
Week 11
Reserve
Week 12
Project 1
Random walks and PDEs
--done!
Project 2
Hydrogen Atom
--done!
Appendices
Some classes of PDEs
Appendix B
to
Lecture 13
--counting the number of negative eigenvalues by applying variational principles
Appendix C
to
Lecture 13
--direct counting the number of negative eigenvalues
Appendix D
to Week 1--analyzing traffic flow
Appendix E
Eigenvalues of Laplacian in the disk and a ball
Exploded (Incomplete) View of APM346