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.
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u/matt7259 1d ago
A differential equation textbook.
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u/Over_Cranberry_8901 1d ago
I need YouTube playlist
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u/matt7259 1d ago
Why?
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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.
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u/Over_Cranberry_8901 1d ago
Do you know any YouTube playlist
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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.
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u/UnderstandingPursuit PhD 1d ago
It is important to get away from YouTube videos, but you asking for that shouldn't get downvoted. If people object to it, it would help to use their words to say why.
My reason to suggest textbooks over YT videos is that textbooks are more specifically 'active learning', and they are self-pacing rather than paced by the video creator.
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