To the MHF Community,
It's been over a year since I have updated this differential equations tutorial of mine.
Some of you have PMed me about errors/typos found in this tutorial, why certain topics aren't covered, etc. But I just haven't had the time lately to fix them or add missing topics since most of my time is devoted to my coursework (since I'm a full time Ph.D. student now). However, this summer (starting in June), I will be redoing this entire differential equations tutorial and re-release it as a mini-book (it may not be mini when I'm through with it... ) of some kind; meaning, it will have the theory explained in a more, precise detail. It will also have examples illustrating various techniques outlined in each section as well as a few exercises for you to attempt. At first I will not include solutions to these exercises, but in the months after releasing this to the public on MHF I will include solutions to selected exercises outlined in each section/chapter (the format is still yet to be decided).
The chapter outline will be something like:
Chapter 0 - Calculus Review
Part 1 - Ordinary Differential Equations (to be released end of summer 2011)
Chapter 1 - First Order Differential Equations
Chapter 2 - Second and Higher Order Differential Equations
Chapter 3 - Solving Differential Equations by Numerical Methods
Chapter 4 - Matrix Methods and Systems of Differential Equations
Chapter 5 - Laplace Transforms
Chapter 6 - Power Series Solutions to Differential Equations
Part 2 - Partial Differential Equations (to be released sometime in 2012)
Chapter 7 - Introduction to Partial Differential Equations
Chapter 8 - Fourier Series
Chapter 9 - The Wave, Heat, and Laplace Equations
Chapter 10 - Solving Partial Differential Equations by Various Methods
Chapter 11 - Green's Functions
Chapter 12 - Solving Partial Differential Equations by Numerical Methods
If you would like to contribute to this project, send me a PM and we can discuss it in more detail. If I use any of your work in my book, you will be acknowledged.
I will close this thread in the meantime, and I will post updates when I'm able.