Video Lectures for Partial Differential Equations, MATH 4302
Lectures
Resources for PDEs
Course Information
Home Work
A list of similar courses
--------------------------------------------------------------------------------------------------
Resources for Ordinary Differential Equations
ODE at MIT. Video of lectures given by Arthur Mattuck and Haynes Miller, mathlets by Huber Hohn, at Massachussette Institute of Technology. Includes transcript, tools, exams, etc.
ODE at AASU. Narrated slides for ODEs given by Selwyn Hollis at Armstrong Atlantic State University.
Differential Equations with Boundary Value Problems. text , software, homework, livemath by Selwyn Hollis. Use Internet Explorer and install LiveMath plugin. Or first make sure plugin works for your browser.
Differential Equation Movies . Animation of ODE problems, by Selwyn Hollis.
ODE Tools at JHU. Java tools for course given by Chikako Mese at John Hopkins University.
Interactive Differential Equations Addison Wesley Pearson set of applets for ODE.
ODE Text By Harry Watson Jr.
ODE notes By Paul Dawkins.
ODE solver Gidoin Fabienne, Jorro Remi, WIMS, France.
Direction Field Plotter John Polking, Rice University.
Direction Field Software. go to bottom of page, type in right hand side of your equation, using x and y.
Phase for Autonomous ODEs Richard Mansfield, Frits Beukers.
Harmonic Oscillator Eric Woolgar, University of Alberta. Graph of solution of IVP ay"+by'+cy=0, y(0), y'(0).
Graphical solver for Second-Order ODEs. your variables are t, u, v=u'.
--------------------------------------------------------------------------------------------------
Resources for Calculus I
Function Analyzer.
Integrator.
Calculator.
--------------------------------------------------------------------------------------------------
General Purpose Mathematics Software
Scilab a free numerical package similar to Matlab.
Maxima a free symbolic computer algebra system .
--------------------------------------------------------------------------------------------------
Resources for Physics
physics applets Walter Fendt
physics applets Wolfgang Christian, Davison College.
physics applets Scott Schneider, LTU.
--------------------------------------------------------------------------------------------------
Resources for Partial Differential Equations
Applets:
Heat/Diffusion/Parabolic Equations
B. Terrell, Heat equation with modifiable input
J. Feldman, Heat Equation
J. Blanchard, Parabolic Eq
B. Terrell, 2d heat equation

Fourier Series
Fourier Series Lab 1 change the first 21 coefficients of a mixed fourier series to make a function. Has basic samples.
Basic operations on basic functions and their effect on the the fourier series.
Fourier cosine series with phase shift
Fourier series for arbitrary functions you provide the code for function.

Wave/Hyperbolic
J. Feldman, Two Examples for Fourier Series
J. Feldman, An Example of Wave Equation on a String
J. Feldman, An Example of Wave Equation on a String
J. Feldman, An Example of Wave Equation on a String
J. Feldman, Telegraph Equation
S. A. Sarra, Weak Solutions and Shocks
IsoSpectral Domains
C. Nyack, 1D Wave with Partial Fourier Sum
Other Equations
P. Garrett, Klein Gordon Wave

Texts:
P. J. Olver, Lecture Notes on PDEs
H. R. Beyer, Introduction to Classical PDEs
L. N. Trefethen, Finite Difference and Spectral Methods for ODe and PDEs
Matthew J. Hancock, Linear PDEs
J. Nearing, Mathematical Tools for Physics
E. M. Harrell, J.V. Herod, Linear Methods of Applied Mathematics
A. Hood, Applied Mathematics and PDEs
B. Birnir, Elementary PDEs and Applications Needs postscript viewr.
J. Herod, Maple Based PDE free subscription needed.

Numerical Methods for PDEs B. K. Driver, PDE Lecture Notes
J. Herod, PDE
T. Driscoll, Isospectral Domains
S.A. Sarra, Method of Characterstics with applications to Conservation Laws.

Software and Code:
J. Cooper, Intoduction to PDEs with Matlab
J. C. Adams, MUDPACK, Multigrid Software for Elliptic PDEs
Clawpack, Conservation Laws Package
PETSC, Solver Suite for PDEs

Listings:
Intute listing for PDEs
--------------------------------------------------------------------------------------------------
Lectures
--------------------------------------------------------------------------------------------------
Lecture 1
Classification of PDEs, To be uploaded
Linear vs Non-Linear , Homogeneous vs non-homogeneous, constant coefficient vs variable coefficent, order, initial conditions, boundary conditons.
--------------------------------------------------------------------------------------------------
Lecture 2
Boundary Conditions
explanation for several types:
Dirichlet Type: temperature of end point given,
Robin Type: temperature of surrounding area given,
Neuman Type: heat flux given, including complete insulation.
Newton Law of cooling and Fourier Law.
--------------------------------------------------------------------------------------------------
Lecture 3
Derivation of Heat Equation
Using Conservation of Energy to derive diffusion equation. Energy density, specific heat, thermal capacity, diffusivity.
--------------------------------------------------------------------------------------------------
Lecture 4 a
Separation of variables 1
Explanation of basic steps. Zero temperature at end points. Superposition Principle. Fourier Sine Expansion.
--------------------------------------------------------------------------------------------------
Lecture 4 b
Separation of variables 2
Funamental solutions. Orthogonality. Homogeneous boundary conditions.
--------------------------------------------------------------------------------------------------
Lecture 4 c
Separation of variables 3
Dirichlet, Neumann, Robin, Mixed boundary conditions. Fundamental solutions for the Neumann BC. An example of mixed BC.
--------------------------------------------------------------------------------------------------
Lecture 4 d
An example of mixed BC
.
--------------------------------------------------------------------------------------------------
Lecture 5
NonHomogeneous Boundary Conditions 1
Constant dirichlet boundary conidtions, temperature of end points given as nonzero. steady state and transient solutons.
--------------------------------------------------------------------------------------------------
Lecture 6
Introduction to Wave / Hyperbolic Equations
Derivation of U_tt = c^2 U_xx for the oscillations of a string.
--------------------------------------------------------------------------------------------------
Lecture 7
Solution of wave equation on infinite domain. Verification of solution.
--------------------------------------------------------------------------------------------------
Lecture 8
Graphical description of the solution of Wave Equation for infinite domain. Part 1 u(x,0)=f(x), U_t(x,0)=0
--------------------------------------------------------------------------------------------------
Lecture 9
Graphical description of the solution of Wave Equation for infinite domain. Part 2 u(x,0)=0, U_t(x,0)=g(x)
--------------------------------------------------------------------------------------------------
Lecture 10
D'Alambert's Solution of Wave Equation, Part 1
--------------------------------------------------------------------------------------------------
Lecture 11
Solution of Wave Equation on semi-infinite domains
--------------------------------------------------------------------------------------------------
Lecture 12
Solution of Wave Equation on finite domains
--------------------------------------------------------------------------------------------------
Lecture 13
Wave Equations in Two Dimensions, Part 1
--------------------------------------------------------------------------------------------------
Lecture 14
Wave Equations in Two Dimensions, Part 2
--------------------------------------------------------------------------------------------------
Lecture 15
Introduction to Bessel Function
--------------------------------------------------------------------------------------------------