Maple/Lesson 10: Using Maple in Calculus, PDEs and ODEs

Chapter 10 : Using Maple in Calculus, ODEs and PDEs

Symbolic Integration with Maple

Tired of looking up tables of integrals? In case, you don't have access to Maple, here's a cheatsheet I've found extremely useful for my reference: Tables of Integrals, Trig Identities, Advanced Mathematics, and much more Want to check the correctness of your hand-worked solution? Want an easy way to generate/learn mathematical LaTeX?

I like to make sure that I typed the integral in right before asking Maple to actually evaluate it for me.

>Int((cos(omega*t + phi))^2,t=0..2*pi);

$\underset{0}{\overset{2\pi }{\int }}{\cos (\omega t+\varphi )}^{2}dt$

Just switch the case from Int to int for evaluation of the integral.

>int((cos(omega*t + phi))^2,t=0..2*pi);

(the answer is quite a complex expression) (Maple even knows to translate omega and phi to the greek letters!)

Symbolic Differentiation with Maple

>Diff(log(x),x);

$\frac{d}{dx}ln(x)$

Solving partial fraction decompositions with Maple

This is something I've done so many times and is so tedious, that I often use Maple for. math.vanderbilt.edu also had an online version (it is discontinued due to hardware failure)

A borrowed trick from Matlab (using the fundamental theorem of calculus): To integrate it, it will probably have to do a partial fraction expansion, so we let it do the expansion when it integrates, then differentiate to get our rational expression converted/decomposed into partial fractions:

>diff(int((5*x+1) / (x^2-1),x),x);

$\frac{3}{x-1}+\frac{2}{1+x}$

Maple has partial fraction expansion built in, though, if you want to do it directly. The command is

>convert( (5*x+1) / (x^2-1), parfrac, x);

$\frac{3}{x-1}+\frac{2}{1+x}$

I wanted to make a contribution to a piece of software I find extremely useful and help others use it for their needs. Feel free to edit what I've written.

Resource Listing

List of mathematical internet resources