Looking for Textbook Suggestions

[wintermute++]

Funny story, or maybe I'm just dumb and don't understand why my professor is being all petulant about this.

∫∫h(x,y)dA

If z = h(x,y) and h(x,y) = f(x)g(y)

∫∫f(x)g(y)dxdy = ∫f(x)dx∫g(y)dy

I did this on my own while working through some double integral hw. Seems obvious, and the answers were always correct. Used it on the test, got a 0 for each question I did. Was told to prove it for credit, so I did.

No credit given. Now the teacher demands I give him a single page from a textbook with this in it before I can earn credit and I'm pissed because it's not in any of our libraries textbooks, yet I've found googledocs from other universities that show it as an example.

Sooooo please, please. If any of you out there have a textbook with this example in it, please tell me what it is so I can hunt a copy down and not get a fail where I should have had a 92. I will owe you one cookie for your efforts.

 

[lurflurf]

Post your proof. I hope this professor just wants more details, and is not surprised by this result.

That is called Fubini's theorem or Tonelli's theorem. It should be in any calculus book.

http://en.wikipedia.org/wiki/Fubini%27s_theorem
http://mathworld.wolfram.com/FubiniTheorem.html
http://www.math.harvard.edu/~shlomo/
Advanced Calculus by Loomis and Sternberg page 346

 

[wintermute++]

I know of Fubini's Theorem. Surprisingly though, I had to pirate about 25 Calculus textbooks to find my exact proof, written how I did it, and I only found that in a "special case" section in a Stewart textbook.

I only got an 8/10 instead of a 10/10 though, because the professor assumed I was just guessing. Despite my sending him the proof. Whatever, I'm only 1/5 pissed off anymore.

The Professor also warned me about it being a "dangerous" equation for some reason. Any explanation for that?

 

[lurflurf]

It is dangerous if the condition of absolute integrability is ignored, as the result need not hold in that case.