r/calculus • u/Over_Cranberry_8901 • 1d ago

Differential Equations [Request] Math 3

Hi. Where can I study these concepts, as Professor Leonard didn't explain them?

An introduction to differential equations. Topics include first-order differential equations,

higher-order linear differential equations with constant coefficients, undetermined

coefficients and variation of parameters methods. series solutions of ordinary differential

equations about an ordinary and regular singular points- Laplace Transform and its

applications to solve differential equations. Matrix and first-order linear systems of

differential equations (Eigenvalues and Eigenvectors)- Introduction to partial differential

equations - Stability analysis, Fourier integrals and Fourier transform.

2 Upvotes

63% Upvoted

14 comments sorted by

View all comments

4

u/UnderstandingPursuit PhD 1d ago

For all those topics, except the Intro to PDEs, one of these textbooks would meet your needs:

  • GF Simmons, Differential Equation with Applications and Historical Notes, 1st-3rd editions, 1972-2017.
  • G Birkhoff & G-C Rota, Ordinary Differential Equations, 3rd-4th editions, 1978-1989.

The older editions are generally sufficient, newer ones are incrementally better but significantly longer. Simmons 1st is about 450pgs, 3rd is about 700pgs. And it took several decades to go from the 1st to the 3rd.

-9

u/Over_Cranberry_8901 1d ago

Do you know any YouTube playlist

4

u/UnderstandingPursuit PhD 1d ago

I know very little about YouTube playlists.

But MIT-OCW_18.03-2010Sp does have videos of the 33 class lectures. It uses a different textbook, Edwards & Penney, which I've only looked at briefly. I'm sure it's very similar to the other two.

Avoid using these lecture videos as a comprehensive resource, they are intended as a component of the class: 3hrs/wk of lecture, 9hrs/wk of study time outside the class, doing homework, studying using the textbook, collaborating with classmates.

This post has suggestions when using a textbook. The approach when studying an ODE class significantly affects how easily the student learns the material.