Useful Tricks for Calculus & Vector Calculus

[glebovg]

Can anyone list some useful tricks for calculus and vector calculus.

i.e. sneaky substitutions, changing limits of integration when changing coordinate systems, parametrization of curves, surfaces, and volumes etc.

 

[Nebuchadnezza]

I will only answer here.

What you are asking for is something which I love. Integration. It is a beautiful art.

The only thing that can make you better at it is solving problems. Below is a list of my favourite integrals. Also a link to a few pages where we tackle hard integrals.

https://www.physicsforums.com/showthread.php?t=149706

Here is another page with integral solutions. Press the "Werner integral challenges" pages

http://www.artofproblemsolving.com/Forum/viewtopic.php?f=296&t=429543

http://www.artofproblemsolving.com/Forum/viewtopic.php?f=296&t=424534

http://www.artofproblemsolving.com/Forum/viewtopic.php?f=296&t=423162

A few diferent pages

http://www.artofproblemsolving.com/Forum/viewtopic.php?f=296&t=420023

http://www.artofproblemsolving.com/Forum/viewtopic.php?f=296&t=384995

Quite a big list here too

http://www.artofproblemsolving.com/Forum/resources.php?c=87&cid=184

Integral bee

http://www.mathhelpforum.com/math-help/f25/2011-mit-integration-bee-qualifying-test-169383.html

http://www.mathhelpforum.com/math-help/f25/2011-mit-integration-bee-qualifying-test-169383.html

Greek website, really good

http://www.mathematica.gr/forum/viewtopic.php?f=9&t=7842&start=20

Norwegian thread and posts. The math is universal though

http://www.matematikk.net/ressurser/matteprat/viewtopic.php?t=28110&start=15

http://www.matematikk.net/ressurser/matteprat/viewtopic.php?t=24242&postdays=0&postorder=asc&start=0

 

[HallsofIvy]

The really useful "trick" is understanding!

 

[glebovg]

What about changing limits of integration when changing coordinate systems, parametrization of curves, surfaces, and volumes?

 

[glebovg]

Does anyone know any useful vector calculus tricks?