General question on Differential equations

Saladsamurai
Messages
3,009
Reaction score
7
I was just wondering...I usually like to get a head start on future classes (as opposed to past classes:smile:...my own jokes kill me!) and was wondering what kind of material I should really focus on for differential equations? I feel like I have a pretty firm grasp on the key concepts of calculus through Calculus 2 (this covers up to Taylor/Maclaurin polynomials at my school). But, are there any specific areas of calculus (or other maths) that could give me an edge?

Advice is appreciated. Thanks a bunch,
Casey
 
Physics news on Phys.org
Maybe the Diff eqs forum would have been a better spot, eh? :blushing:
 
Differential equations is pretty easy compared to multivariable calculus and linear algebra. Exponentials come up everywhere in differential equations so be sure you know every about natural logs and e. Try learning how to solve homogeneous first-order and second-order differential equations with constant coefficients--you need nothing fancy to solve these.
 
Thanks ehrenfest, I think I saw some of those in my calcululs text in one of the chapters we didn't cover.

Casey
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top