Maple/Lesson 10: Using Maple in Calculus, PDEs and ODEs
From Wikibooks, the open-content textbooks collection
Contents |
[edit] Chapter 10 : Using Maple in Calculus, ODEs and PDEs
[edit] 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?
To make sure that the typed integral is right, before asking Maple to actually evaluate it, use the inert command Int:
>Int((cos(omega*t + phi))^2,t=0..2*Pi/omega);
To evaluate the integral use the command value.
>value(%);
[edit] Symbolic Differentiation with Maple
The inert differentiation operator is Diff:
>Diff(ln(x),x);
>value(%);
[edit] 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);
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);
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.
