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Differential Equations with Boundary Value Problem

http://www.math.armstrong.edu/faculty/hollis/dewbvp

By S. Hollis (Prentice Hall, 2002). Overview of contents, errata, software and link to purchasing page.

http://math.arizona.edu/~lega/583/Fall98/lectnotes/GF1.html

Lecture notes introducing this technique for solving first and second order differential equations. Scanned (GIF) by Joceline Lega.

Introduction to Ordinary Differential Equations wi

http://math.cl.uh.edu/math/ode/ode.html

Contains a number of ODE labs, and an extremely useful Mathematica Package ode.m which allows series solutions of ODEs.

Pseudo-Differential Operators

http://arxiv.org/abs/math.AP/9906155

These lecture notes cover a first year graduate course that was given on pseudo-differential operators. The calculus on manifolds is developed and applied to prove propagation of singularities and the Hodge decomposition theorem.

Series Solutions to Differential Equations

http://www.math.hawaii.edu/~lee/calculus/#Series-Sol

A set of downloadable lectures.

Vibrating Drumhead

http://www.ma.iup.edu/projects/CalcDEMma/drum/drum.html

A set of Mathematica packages which outline solutions of the wave equation in various coordinates.

Waves and Oscillations

http://www.maths.gla.ac.uk/~fhg/waves/

Teaching resources developed by Frances Goldman, University of Glasgow.