01-01-2004 22:22									#1
	mathematics for physicists discussion thread Support Apolyton, buy Alpha Centauri

For the math-physics studs: Do you guys actually have a good command and intutive feel for multivariable calc and PDE? I felt like I could handle integral and differential calc. But I never got the div/grad/curl thing straight. Is that a common issue?

	01-01-2004 22:36									#2
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yeah

	01-01-2004 22:46									#3
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I'd say I have an intuitive feel for vector cal. Taking a class on it, and a few physics classes where it's heavily used would do that to a person. In lots of physics (for instance, electro), it's fundamental. It's suprisingly simple when you get down to it; you've got a few differential operators, and you can map differential forms to a higher/lower order one with these operators, and you get those three neat theorems - and it's all geometrically intuitive. Work with them a little, and you can catch on just fine.

PDE's, no. I don't know how anyone can have a truly intuitive feel for them. I might have a good command depending on how you define "good."

Last edited by Ramo on 01-01-2004 at 22:58

	01-01-2004 23:04									#4
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no problem really

multivariable seems like second nature

but than I had like 3 classes in them in my first two years of college

and of course, I am hard pressed to name a class that I have taken since my freshman (?) year that didn't use Multivariable

I have had a number of classes that dealt with PDE's also, but routinely find myself out of practice in dealing with them (I am right now, for example, did not deal with many this last semester)

Jon Miller

	01-01-2004 23:56									#5
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I also have a hard time with classical E/M.

	02-01-2004 00:09									#6
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So I think part of the problem with me is that I got a B in 3rd semester (multivariable) calc and never really got it down. If I studied it, would I be able to grasp it and have a decent feel for it?

P.s. I was such a geek that I asked for and got a copy of Arfken for Christmas.

	02-01-2004 00:10									#7
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P.s. were there any comments made in the previous copy of this thread?

	02-01-2004 00:12									#8
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Arfken is fine as a review, is crap to learn from though

Jon Miller

	02-01-2004 00:14									#9
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can I recommend Jackson to alleiviate your E&M problems?

Jon Miller

	02-01-2004 00:17									#10
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I think that you probably just need to do problems

two birds with one stone sort of thing

JOn Miller

	02-01-2004 01:22									#11
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Well...for Jackson, can it be studied by somone with my level of knowledge? Or do I need something easier. As for Arfken, it does not have problem solutions. I wonder if there is an answer book that I can buy. What do you suggest to learn from?

	02-01-2004 02:45									#12
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Try Griffiths.

	02-01-2004 02:47									#13
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text name?

	02-01-2004 02:51									#14
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Intro to Electrodynamics I think. It was probably the best text I've used at UT.

	02-01-2004 02:51									#15
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quote: But I never got the div/grad/curl thing straight

To me, it seems a lot more intuitive when its applied to a physical scenario than to a purely mathematical or geometric contemplation.

	02-01-2004 02:51									#16
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good problems? Does it teach?

	02-01-2004 02:55									#17
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Really good book to learn from. I don't think it has that many problems (but they're usually fine) if that's what you're looking for.

	02-01-2004 02:57									#18
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I find problems (and drill) to be an effective tool for learning. Even more so when the concepts are difficult than when they are easily grasped.

	02-01-2004 03:06									#19
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It's been over a year since I've used it, but IIRC it has enough problems to learn from. The real draw is his ability to explain the physical concepts in intuitive terms.

	02-01-2004 03:34									#20
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quote: Originally posted by Ted Striker yeah

me too

	02-01-2004 03:37									#21
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quote: Originally posted by Ramo It's been over a year since I've used it, but IIRC it has enough problems to learn from. The real draw is his ability to explain the physical concepts in intuitive terms.

thanks.

	02-01-2004 04:05									#22
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I will look through my collection

I acutally liked Wangness better as a lower level book

Jon Miller

	02-01-2004 04:07									#23
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I doubt that is really a book. In any case, the vagueness makes the reference useless.

	02-01-2004 04:11									#24
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Wangness is an E&M book

I used it in Undergrad

Jon Miller

	02-01-2004 05:01									#25
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ok

	02-01-2004 05:02									#26
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lots of examples

Jon Miller

	02-01-2004 10:40									#27
	Re: mathematics for physicists discussion thread Avatar Enlargement: We've got the solution

quote: Originally posted by TCO For the math-physics studs: Do you guys actually have a good command and intutive feel for multivariable calc and PDE? I felt like I could handle integral and differential calc. But I never got the div/grad/curl thing straight. Is that a common issue?

You should know what they are pretty intuitively, what the poisson/laplace equation are (i.e. what a "source" or "sink" does to a vector field)

Grad is a really obvious physical quantity; it points in the direction of maximal incline of the function and its length is the derivative in that direction. Think of being on a hill; grad points to the direction which is instantaneously the steepest.

Divergence talks about sources and sinks. Understanding the radial vector field r^-2 (whose divergence is the 3-d dirac delta function) should provide significan understanding.

Curl is slightly more complex.

It basically measures the swirling of a vector field.

Think about the vector field (in the plane) which is purely tangential and which goes as 1/r

Again, the curl of this function is a dirac delta function.

Now think about how you use Greens functions (which are basically superpositions of delta functions) to solve boundary value equations, and how understanding the previous two examples of delta-function div and curl actually give you the whole story.

	02-01-2004 10:43									#28
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quote: Originally posted by TCO Well...for Jackson, can it be studied by somone with my level of knowledge? Or do I need something easier. As for Arfken, it does not have problem solutions. I wonder if there is an answer book that I can buy. What do you suggest to learn from?

If you want to buy a completely solid and very physically intuitive book, buy Griffiths Intro to EM

There is no better undergrad level text that I've seen.

Jackson is not what you want, trust me.

It's a very good book for the rigorously inclined, and excellent for those who want to do complicated problems in agonizing detail.

	02-01-2004 10:45									#29
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You cannot generally buy solutions manuals unless you can show your bona fides (i.e. that you're a prof and not somebody who wants to cheat on homework)

PM me, TCO.

	02-01-2004 10:46									#30
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I looked at griffiths, but didn't use it

I think I liked Wangness better

Jon Miler