I have to teach engineering mathematics soon. Much of it revolves around the development, manipulation, and solution of differential equations. In this post, I have gathered good resources just for this purpose.
Following are a set of lectures by much-revered professor Gilbert Strang on differential equations.
https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/introduction/overview-of-differential-equations
https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/introduction/the-calculus-you-need
By the way, I was wondering that why do we multiply with the exponent while taking derivatives (if you remember the power rule). I looked up on the Internet and found this cool explanation on Coursera.
https://www.coursera.org/learn/calculus1/lecture/WifyU/how-do-we-justify-the-power-rule
https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/response-to-exponential-input
https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/solution-for-any-input
https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/step-function-and-delta-function
https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/response-to-complex-exponential
https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/integrating-factor-for-constant-rate
https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/integrating-factor-for-a-varying-rate
https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/the-logistic-equation
The Stability and Instability of Steady States
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https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/separable-equations
Second Order Equations
Description: For the oscillation equation with no damping and no forcing, all solutions share the same natural frequency. Related section in textbook: 2.1 Instructor: Prof. Gilbert Strang
Forced Harmonic Motion
Description: When the forcing is a sinusoidal input, like a cosine, one particular solution has the same form. But if the forcing frequency equals the natural frequency there is resonance. Related section in textbook: 2.1b Instructor: Prof. Gilbert Strang
Unforced Damped Motion
Description: With constant coefficients in a differential equation, the basic solutions are exponentials. The exponent solves a simple equation. Related section in textbook: 2.3 Instructor: Prof. Gilbert Strang
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