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These are notes for the University of Alberta MATH 201 - Differential Equations course.
I have written these notes for myself, I thought it would be cool to share them. These notes may be inaccurate, incomplete, or incoherent. No warranty is expressed or implied. Reader assumes all risk and liabilities.
Separable equations (lec 1)
Homogenous equations (lec 2)
Linear equations (lec 2-3)
Bernoulli equations (lec 3)
Linear coefficient equations (lec 4)
Exact equations (lec 4-5)
Second order homogenous linear equations (lec 5-7)
Method of undetermined coefficients (lec 8-9)
Variation of parameters (lec 9-10)
Cauchy-Euler equations (lec 10-11)
Reduction of order (lec 11)
Free vibrations (lec 11-12)
Resonance & AM (lec 13-14)
Laplace transform (lec 14-16)
Solving IVP's using Laplace transform (lec 17-18)
(Heaviside) Unit step function (lec 18)
Periodic functions (lec 19)
Convolution (lec 19-20)
Dirak δ-function (lec 21)
Systems of linear equations (lec 21-22)
Power series (lec 22-25)
Separation of variables & Eigen value problems (lec 26-28)
Fourier series (lec 28-29)
Heat equation (lec 30-33)
Wave equation (lec 33-36)
How to solve any DE, a flow chart (Last updated Oct 1st 2023. Needs revision, but it gives a nice overview.)
Big LT table (.png)
Small LT table (.png)
Recommended study material
For the midterm exam, I highly recommend watching this video by The Math Sorcerer: youtube.com/watch?v=kIZpbeE_yTc
From my experience, studying off this video was by far the best use of my time. Try each question yourself and follow his solution to check.
For the final exam, I unfortunately couldn't find good study videos. I recommend studying PDE's hard, solidify your understanding of heat eq, driven heat eq, heat eq with non-zero end points, wave eq, and driven wave eq. Afterwards, I recommend studying power series since it's the next biggest scary monster. Finally, go over the rest of the past topics to fill your understanding and memory if you have the time.
The recommended course textbook when I took the class was: Fundamentals of Differential Equations, R. Kent Nagle, Edward B. Saff and Arthur D. Snider, 9th Edition Which is a good textbook imo, although I didn't use it often.
I mostly studied the material by attending the lectures and then reviewing/revising these typed notes on the bus or at home, often relying on my prof's notes on eclass in case I copied off the whiteboard wrong/couldn't keep up. (eclass is the name of my university's online class management system.)
Of course there may still be mistakes riddled throughout so as of Jan 5th 2024, I'm offering 1$ CAD in bounties for every mistake reported to my email/git repo, at least until supplies last. General editing and formatting changes are also gladly welcomed through the git repository below or by email. Seeing people use these notes and benefitting from it makes me happy, so thanks for sticking around :) and remember to use what you learn for good! And to lead life with honor and integrity and be ethical engineers. Dr. Minev used to never forget to stress the importance of this in his lectures, and I wholeheartedly agree.