Multivariate transformation problem

[Groms14]

I'm having a hard time determining the range in multivariate transformation problems. One particular one is from Krzys' weekly problem from May 14, 2005. If anyone could take a look and explain to me how they figured out the ranges for w and z in the multivariate transformation part of this problem that would be great. Thanks

[krzysio]

I'm having a hard time determining the range in multivariate transformation problems. One particular one is from Krzys' weekly problem from May 14, 2005. If anyone could take a look and explain to me how they figured out the ranges for w and z in the multivariate transformation part of this problem that would be great. Thanks

As you know, I answer questions about my practice problems. What is your question about May 14, 2005 problem? And, judging from just the appearance of your post, you would probably benefit from studying this in the ASM Manual.
Yours,
Krzys'

[Groms14]

I understand everything until the ranges of w and z are figured out. I get that through the transformation 0<w<200 and 0<z<300. But then I get lost when we combine them to get -w<z<500-w as well as -z<w<500-z. And yes I plan on studying the ASM manual but I haven't purchased it yet because I am waiting till I head back to college.

[ctperng]

I understand everything until the ranges of w and z are figured out. I get that through the transformation 0<w<200 and 0<z<300. But then I get lost when we combine them to get -w<z<500-w as well as -z<w<500-z. And yes I plan on studying the ASM manual but I haven't purchased it yet because I am waiting till I head back to college.

The latter two inequalities come from the fact that

0<w+z<500. (note: 200+300 = 500)

ctperng

[Groms14]

The latter two inequalities come from the fact that

0<w+z<500. (note: 200+300 = 500)

ctperng

Then how do you also develop the limits of the three integrals?

[ctperng]

Then how do you also develop the limits of the three integrals?

If you purchase the manual, you might get clear explanation. And the author is always willing to answer your question either in this forum or by email.

If you look at the solutions, you have at least three different ways to solve it. The transformation method, IMO, is not the most intuitive one, especially under the exam condition.

If you want to master integration, you can also look up calculus book for more examples on multiple integrals, on how to arrange the bounds for integrations, etc. These are usually easy to explain by pointing to a graph.

ctperng

[krzysio]

Then how do you also develop the limits of the three integrals?

Please be more specific. All steps are explained there. Tell me please where you stop understanding. Going through these three solutions step by step is a very good educational exercise, try it. When you get stuck and can't understand, send me an e-mail (you can post here, too, but it will take me longer to get to it).
Yours,
Krzys'