Reddit reviews Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Fourth Edition)
We found 26 Reddit comments about Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Fourth Edition). Here are the top ones, ranked by their Reddit score.
Get a copy of Div, Grad, Curl. It will walk you through the math you need.
For multivariable calculus I cannot recommend Div, Grad, Curl and All That enough. It’s got wonderful physically motivated examples and great problems. If you work through all the problems you’ll have s nice grasp on some central topics of vector calculus. It’s also rather thin, making it feel approachable for self learning (and easy to travel with).
A commonly used book for this exact purpose is Div, Grad, Curl by Schey.
You're English is great.
I'd like to reemphasize /u/Plaetean's great suggestion of learning the math. That's so important and will make your later career much easier. Khan Academy seems to go all through differential equations. All of the more advanced topics they have differential and integral calculus of the single variable, multivariable calculus, ordinary differential equations, and linear algebra are very useful in physics.
As to textbooks that cover that material I've heard Div, Grad, Curl for multivariable/vector calculus is good, as is Strang for linear algebra. Purcell an introductory E&M text also has an excellent discussion of the curl.
As for introductory physics I love Purcell's E&M. I'd recommend the third edition to you as although it uses SI units, which personally I dislike, it has far more problems than the second, and crucially has many solutions to them included, which makes it much better for self study. As for Mechanics there are a million possible textbooks, and online sources. I'll let someone else recommend that.
Not sure if they qualify as "beautifully written", but I've got two that are such good reads that I love to go back to them from time to time:
let me give you a shortcut.
You want to know how partial derivatives work? Consider a function with two variables: f(x,y) = x^2 y^3, for a simple example.
here's what you do. Let's take the partial derivative with respect to x. What you do, is you consider all the other variables to be constant, and just take the standard derivative with respect to x. In this case, the partial derivative with respect to x is: 2xy^3. That's it, it's really that easy.
What about taking with respect to y? Same thing, now x is constant, and your answer is 3x^2 y^2.
This is an incredibly deep topic, but getting enough of an understanding to tackle gradient descent is really pretty simple. If you want to full on jump in though and get some exposure to way more than you need, check out div curl and grad and all that. It covers a lot, including a fair amount that you won't need for any ML algorithm I've ever seen (curl, divergence theorem, etc) but the intro section on the gradient at the beginning might be helpful... maybe see if you can find a pdf or something. There's probably other good intros too, but seriously... the mechanics of actually performing a partial derivative really are that easy. If you can do a derivative in one dimension, you can handle partial derivatives.
edit: I misread, didn't see you were a junior in highschool. Disregard div curl grad and all that, I highly recommend it, but you should be up through calc 3 and linear algebra first.
To change my advice to be slightly more relevant, learn how normal derivatives work. Go through the Kahn Academy calc stuff if the format appeals to you. Doesn't matter what course you go through though, you just need to go through a few dozen exercises (or a few hundred, depending on your patience and interest) and you'll get there. Derivatives aren't too complicated really, if you understand the limit definition of the derivative (taking the slope over a vanishingly small interval) then the rest is just learning special cases. How do you take the derivative of f(x)g(x)? f(g(x))? There's really not too many rules, so just spend a while practicing and you'll be right where you need to be. Once you're there, going up to understanding partial derivatives is as simple as I described above... if you can take a standard derivative, you can take a partial derivative.
Also: props for wading into the deep end yourself! I know some of this stuff might seem intimidating, but if you do what you're doing (make sure you understand as much as you can instead of blowing ahead) you'll be able to follow this trail as far as you want to go. Good luck, and feel free to hit me up if you have any specific questions, I'd be happy to share.
It's useful for Electromagnetic physics. Surface integrals are used for finding the flux through a Gaussian surfaces so you can use Gauss' Law on non-symmetrical surfaces. Line integrals are used with Ampere's Law to find the magnetic flux. Once you learn the mechanics of working with multivariable calculus, you should read "Div, Grad, Curl and All That"
Are you familiar with Div, Grad, Curl, & All That. If not you'd probably enjoy it.
I looked at the free pages on Amazon and it does seem a bit wordier than the physics books I remember. It could just be the chapter. Maybe it reads like a book; maybe it's incredibly boring :/
If money isn't an issue (or if you're resourceful and internet savvy ;) you can try the book by Serway & Jewett. It's fairly common.
http://www.amazon.com/Physics-Scientists-Engineers-Raymond-Serway/dp/1133947271
As for DE, this book really resonated with me for whatever reason. Your results may vary.
http://www.amazon.com/Course-Differential-Equations-Modeling-Applications/dp/1111827052/ref=sr_1_2?s=books&ie=UTF8&qid=1372632638&sr=1-2&keywords=differential+equations+gill
If your issue is with the technical nature of textbooks in general, then you'll either have to deal with it or look for some books that simplify/summarize the material in some way. The only example I can come up with is:
http://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161/ref=sr_1_1?s=books&ie=UTF8&qid=1372632816&sr=1-1&keywords=div+grad+curl
Although Div, Grad, Curl, and all That is intended for students in an Electromagnetics course (not Physics 2), it might be helpful. It's an informal overview of Calculus 3 integrals and techniques. The book uses electromagnetism in its examples. I don't think it covers electric circuits, which are a mess of their own. However, there are tons of resources on the internet for circuits. I hope all this was helpful :)
Haven't used it myself, but you might want to check out Div,Grad,Curl by Schey.
For vector calculus, you might enjoy the less formal British text Div, Grad, Curl, and All That by H. M. Schey; for group theory in brief, consider the free textbook Elements of Abstract and Linear Algebra by Edwin H. Connell.
Alternatives to Schey's book include the much more formal Calculus on Manifolds by Michael Spivak, which does have more exercises than Schey but uses most of them to develop the theory, rather than as the mindless drills that fill an ordinary textbook; Michael E. Corral's free textbook Vector Calculus isn't huge but is written closer to an ordinary textbook.
For vector calculus: Div, Grad, Curl, and All That: An Informal Text on Vector Calculus
For complex variables/Laplace: Complex Variables and the Laplace Transform for Engineers - Caution! Dover book! Slightly obtuse at times!
For the finite difference stuff I would wait until you have a damn good reason to learn it, because there are a hundred books on it and none of them are that good. You're better off waiting for a problem to come along that really requires it and then getting half a dozen books on the subject from the library.
I can't help with the measurement text as I'm a physicist, not an engineer. Sorry. Hope the rest helps.
Is it this one?
This is the best damn self study book I have ever seen on the subject and think it does better than the latter half of Math 53 in setting up many of the key concepts.
It is short, to the point, and from the outset makes the connections to EM abundantly clear. It is not difficult to find copies of that text online.
I thought of some books suggestions. If you're going all in, go to the library and find a book on vector calculus. You're going to need it if you don't already know spherical coordinates, divergence, gradient, and curl. Try this one if your library has it. Lots of good books on this though. Just look for vector calculus.
Griffiths has a good intro to E&M. I'm sure you can find an old copy on a bookshelf. Doesn't need to be the new one.
Shankar has a quantum book written for an upper level undergrad. The first chapter does an excellent job explaining the basic math behind quantum mechanics .
I found the book Div Grad Curl and All That to explain it pretty well. The book is short enough to read through in a couple hours.
As others have mentioned, there are a lot of good books on Math Methods of Physics out there (I used Hassani's Mathematical Methods: For Students of Physics and Related Fields).
That said, if you're having trouble with calculus, I'd recommend going back and really understanding that well. It underlies more or less all the mathematics found in physics, and trying to learn vector calculus (essential for E&M) without having a solid understanding of single-variable calculus is just asking for trouble.
There are a number of good books out there. Additionally, Khan Academy covers calculus very well. The videos on this page cover everything you'd encounter in your first year, and maybe a smidge more.
Once you move on to vector calculus, Div, Grad, Curl and All That is without equal.
I'm preparing to go from a pure maths/stats background to an applied maths graduate program in the fall, and I bought both of these books:
Hoping they'll help me when I get home to read them, maybe they'll help you too? The Amazon feedback seems pretty positive. Good luck!
When I took EM in addition to Cheng the professor suggested getting Div, Grad, Curl and all of that. I found that to be alot of help in solidifying the math and intuition needed.
Div, Grad, Curl, and All That is a good way to shore up your knowledge of vector calc.
http://www.amazon.com/dp/0471725692/ref=wl_it_dp_o_pd_S_ttl?_encoding=UTF8&colid=2UCFQZHNW5VVF&coliid=I1RPWVCSMOOV09 is one good suggestion, I've seen around here. It's on my wishlist and the book that I intend to work from.
Now I always struggled with vector calculus and its motivations. So I have this one waiting for me as well http://www.amazon.com/dp/0393925161/ref=wl_it_dp_o_pC_nS_ttl?_encoding=UTF8&colid=2UCFQZHNW5VVF&coliid=I20JETA4TTSTJY since I think it covers a lot of the concepts that I had the most trouble with in calc 3
There's a book called Div, Grad, Curl and All That, here is an Amazon link. It's an informal approach to vector mathematics for scientists and engineers and it's pretty readable. If you're struggling with the math, this is for you :) All their examples are EM too.
It's also a good idea to get a study group together. The blind leading the blind actually do get somewhere. :)
Calc 3 was series for us, 4 was multivariable. We were quarters with summer quarter being optional so it was really trimesters for most people. Vector calc was basically taught from the book Div, Grad, Curl and All That. So it was useful prior to going into electrodynamics, which was also 4th year.
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EDIT: Added link.
Try this.
But really it comes with practice, the more you use it, the better you get at reading it and comfortable with it. In my case at least.