Wanting to get into nonlinear equations

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To effectively study nonlinear equations and dynamics, a solid foundation in Calculus and Differential Equations is essential. Recommended resources include "Differential Equations" by Blanchard, Devaney, and Hall, which introduces nonlinear equations, and the two-volume series "Perspectives of NonLinear Dynamics" by E.A. Jackson for deeper insights. A typical study path involves mastering Trigonometry, Analytical Geometry, and progressing through Calculus I and II before tackling Differential Equations. The course requirements can vary significantly, so it's important to adapt your learning based on the specific areas of nonlinear mathematics you wish to explore. Ultimately, a tailored study plan that builds on these fundamentals will facilitate a deeper understanding of nonlinear dynamics.
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What's the best study plan to get into nonlinear equations/dynamics, etc. Let's say we start with Calculus... how far should I go?
Differential Equations afterwards?
What's a typical course tracking into such math?
 
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gambit7 said:
What's the best study plan to get into nonlinear equations/dynamics, etc. Let's say we start with Calculus... how far should I go?
Differential Equations afterwards?
What's a typical course tracking into such math?

Good for you Gambit! That's where all the interesting things happen in my opinion. First know Calculus and Elementary DEs really well. "Differential Equations" by Blanchard, Devaney, and Hall is a good introductory DE text which also covers non-linear equations at a basic level.

An excellent two-volume series is "Perspectives of NonLinear Dynamics" by E.A. Jackson.
 
saltydog said:
Good for you Gambit! That's where all the interesting things happen in my opinion. First know Calculus and Elementary DEs really well. "Differential Equations" by Blanchard, Devaney, and Hall is a good introductory DE text which also covers non-linear equations at a basic level.

An excellent two-volume series is "Perspectives of NonLinear Dynamics" by E.A. Jackson.

So I figure shore up on the Trigonometry, then Analytical Geometry and Calc. I, Calc. II, then Dif. Eq. (dif E.Q. for all u college people). THEN I can start to specialize? That's where the area gets grey to me (the color grey seems to describe nonlinear math pretty well). Different course prospectus' seem to require different levels of knowledge, there's no real definitive approach, you just have to hope you know enough. Also many of the sylabii I've seen cover wider areas of math including nonlinear equations, and I look to just focus on those.
Looks like your ideas will work though. Thanks!
Maybe in a years time I'll have mastered the art of vacuum fluctuations and the veritable aether of the universe. :bugeye:
 
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