Preparing for Differential Equations: Tips for John in PDX

[john_in_pdx]

Hey peeps,

I'll be taking diff-eq next quarter, and I was wondering what I need to do to prep myself for it. I am currently in Vector Calc, but I was wondering what are some things I should practice so I can hit the ground running when the class starts.

Thanks in Advance,

John In PDX

 

[dextercioby]

1.Differentiation of functions with one or more variables.
2.Integrations of functions (especially substitutions).
3.Good knowledge of trigonometry:circular and hyperbolic,hopefully u won't need elliptic one.
4.Fourier and Laplace transformations.Fourier series.
5.Complex analysis.Residue's theorem.
6.Special functions:all particular cases of Gauss' hypergeometric functions.


Daniel.

 

[john_in_pdx]

"4.Fourier and Laplace transformations.Fourier series.
5.Complex analysis.Residue's theorem.
6.Special functions:all particular cases of Gauss' hypergeometric functions."

Wouldn't this be taught in an intro course? You wouldn't be expected to know this going in.

 

[dextercioby]

So it should be normal,but course structure differs from case to case.Some of them assume having prior knowledge from a course on functional analysis.

Daniel.

 

[arildno]

If this is to be the first time you see diff eqs, then, IMO, the single most important thing you understand from what you have learned so far is:

THE CHAIN RULE OF DIFFERENTIATION

In particular, you should understand how this is coupled to the integration technique known as "substitution"

There is, of course, a lot more you need to know, but I've met quite a few students who become confused with the way that diff.eqs are solved, simply because they have failed to understand the above-mentioned issues.

To give you a hint:
When your lecturer starts talking about "separable" differential equations, pay close attention to how this is related to the chain rule&substitution integration technique.

 

[john_in_pdx]

Thanks arildno. That's the type of advice I was looking for.

 

[HallsofIvy]

I consider Linear Algebra a pre-requisite for differential equations. The whole theory of linear differential equations (which is most of introductory differential equations) is based on Linear Algebra.

 

[john_in_pdx]

I had Linear ALgebra last term, so I think I can handle that.

Thanks though for the reccomendation.