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https://en.wikipedia.org/wiki/Gradshteyn_and_Ryzhik

SCNR

ED: Here’s a great review:

> I bought Gradshteyn & Ryzhik because I had to write an answer to some
> homework problem in some physics class that I took. The problem had
> contorted itself into a perverse elliptic integral and its recovery
> was beyond my means, so I went to the bookstore, looked for something
> fat and Soviet, and found this gem. I forked over the cash for it,
> figuring that it was a long-term investment.
>
> I took it home and dutifully plagiarized some of its lines to satisfy
> my physics professor. For the next few months, that was the mode in
> which I used this book: read physics problem, translate into elliptic
> or hypergeometric beast, look up answer in G&R, cover up my tracks,
> get 9 or 10 points on the problem. Occasionally, I would own up to
> having looked something up.
>
> The book served its purpose well. Subsequently, I studied some
> integrals of the spinning top that were more or less right out of
> Nikiforov's book on special functions (another excellent source for
> those of you that would like to "earn" a PhD), and G&R stood well by
> its side. Indeed, I discovered how much fun it was to look up an
> integral whose complicated solution had been derived elsewhere, and
> then to look for patterns by analyzing the immediate neighbors of the
> given integral on the preceding and subsequent lines in G&R.
>
> After I was done with answering questions from physics professors, the
> book sat on the shelf taking up more room than several of its
> neighbors put together. Nonetheless, its binding was good, its
> typesetting clear, and its terse and copious stream of forbidding
> integral forms was pleasing to the eye.
>
> Some time passed, and one day I asked myself just what would motivate
> anybody to write such a large collection, so I started rummaging
> through its pages looking for a pattern. I realized that its
> organization was excellent (which would explain why I was able to find
> the answers for my homework), and I also found some sections that were
> just plain fun. The very beginning lists some sums of infinite series
> that can be derived during lunch or while waiting for a friend at a
> cafe (e.g. sum of k^3 = [1/2(n)(n+1)]^2 ). Then one can read about
> numbers and functions named after Euler, Jacobi, Bernoulli,
> Catalan... each line, more or less, is cross-referenced, so after you
> have given up trying to derive that darned product representation of
> the gamma function, you can go to the book in the library and see how
> Whittaker did it.
>
> After about 15 years of owning this book, I am nowhere near done with
> it. If you like math, and you want insurance against being bored, this
> book just might do the trick. As a bonus, it puts cute matrix stuff in
> the back (e.g. the "circulant") which one can read when desiring a
> break from the integrals. I know the book seems expensive, but think
> of if as spending about two bucks a year on it.
>
> I see that one can now obtain a CDRom version of G&R. An intriguing
> option, specially because it outputs in TeX; but really, how can
> anyone resist the large, stubby charm of its paper version?
>
> G&R can help you to deal with members of the opposite sex. I once used
> it to scare away a girlfriend that was becoming much too annoying, by
> pretending to be thickly engrossed in the process of memorizing every
> single integral in the "special functions" chapters. As for my mother,
> she was particularly proud of me when I showed her that I could
> actually understand "randomly selected" pages from this book (I don't
> suppose that I am giving anything away by remarking that books open
> naturally on sections that have been previously examined).
>
> For those of you that are concerned about home security, G&R is also a
> weapon. Some people surround themselves with baseball bats or, if they
> are particularly reckless, a handgun or two... I prefer to keep a
> fully-loaded G&R by my pillow, which I can hurl at any prowler at a
> moment's notice. Its shape is surprisingly well adjusted to the hand
> for the purposes of hurling, and if the covers are bound by a rubber
> band, the book maintains its shape quite stably as it sails across the
> room. Sell your Smith & Wesson and buy yourself a Gradshteyn &
> Ryzhik. You won't regret it.

https://www.amazon.ca/Table-Integrals-Products-I-Gradshteyn-ebook/dp/B01253U252

OK, then let's try this again, this time using more calculus and less topology-specific results. I'm going to be using LaTeX markup here; see the sidebar to /r/math for a free browser plugin that'll translate my code into readable mathematics.

The following is from Michael Spivak's Calculus on Manifolds, and it's pretty close to the result you want, but with more restrictions in terms of differentiability and such:

• Problem 2-37.
  
  (a) Let [; f \colon \mathbf{R}^2} \to \mathbf{R} ;] be a continuously differentiable function. Show that [; f ;] is not 1-1. Hint: If, for example, [; D_1 f(x,y) \neq 0 ;] for all [; (x,y) ;] in some open set [; A, ;] consider [; g \colon A \to \mathbf{R}^2 ;] defined by [; g(x,y) = \left( f(x,y), y \right). ;]
  
  (b) Generalize this result to the case of a continuously differentiable function [; f \colon \mathbf{R}^n \to \mathbf{R}^m ;] with [; m<n. ;]
  
  The basic idea for (a) is that if there were such an continuously differentiable injection [; f \colon \mathbf{R}^2 \to \mathbf{R}, ;] then (1) we can find some subset [; A \subseteq \mathbf{R}^2 ;] such that (depending on your convention for notation)
  
  [; D_1 f(x,y) = \partial_1 f(x,y) = \partial_x f(x,y) = \frac{\partial f}{\partial x} (x,y) \neq 0 ;]
  
  for all [; (x,y) \in A, ;] and (2) the function [; g \colon A \to \mathbf{R}^2 ;] must have a local continuously differentiable inverse. (This is by the Inverse Function Theorem.)
  
  The problem, however, arises when you consider the actual form of a local inverse for [; g, ;] since [; g^{-1} ;] will be independent of the second coordinate. Accordingly, [; g ;] cannot be injective, whence [; f ;] cannot be injective.
  
  I imagine the generalization to part (b) is similar. The important thing here is that given a function
  
  [; f \colon \mathbf{R}^m \times \mathbf{R}^n \to \mathbf{R}^m, \text{ where } m<n, ;]
  
  one can construct the associated function
  
  [; \begin{align*}<br /> g \colon \mathbf{R}^m \times \mathbf{R}^n &amp;amp;\to \mathbf{R}^m \times \mathbf{R}^n\\<br /> (\mathbf{x}, \mathbf{y}) &amp;amp;\mapsto \left( f(\mathbf{x},\mathbf{y}), \mathbf{y} \right).<br /> \end{align*} ;]
  
  In the above example, we're considering the case [; m=n=1, ;] and we're considering the equivalence [; \mathbf{R}^1 \times \mathbf{R}^1 \simeq \mathbf{R}^2. ;]
  
  The advantage is that [; g ;] now maps between two spaces of the same dimension, so one can often apply the Inverse Function Theorem. (In fact, this is a common way to deduce the Implicit Function Theorem from the Inverse Function Theorem, so you see this technique often enough that it's worth your time to remember it.)
  
  These exercises require stronger assumptions—i.e., continuous differentiability rather than mere continuity—but perhaps this'll at least be a bit more accessible because it doesn't invoke quite so much topology. Hope this helps, and good luck!

One thing I'd recommend is getting Differential Equations in 24 Hours it is a really good primer on a lot of topics that are likely to come up. I don't know when you are going to start, but if you have a week or two to really devote to before the class, then looking over this could be helpful. It is also just a good book to have on hand.

I dont know much about boot camp, but it sounds like having a physical book will be your best bet.

Personally, my favorite text book to use is Calculus: an Intutitive Approach by Morris Kline, but you might want something more advanced than that.

Hey!

So, the topics you listed are all covered in a Calculus I class. There are some texts that are specific to calc I, but most (in my experience) have the whole shebang, up through Calc III and maybe into some basic diff. eqns.

Larson's Calculus of a Single Variable is availible for $13 as an E-book, if you're okay with that. This version only goes through Calc I, but it's a bit cheaper than the full book. I personally don't love this book, but a lot of people swear by it. It gives lots of application examples, but I don't think they do a great job showing how they work through solutions. This is best as a supplement to a class that uses problems from that book.

My personal favourite is Dover's Calculus: An Intuitive and Physical Approach. This book is much more theorem-oriented and I think it stands better alone than Larson's calculus. I taught myself from this book.

I have made so many mistakes of similar nature, and I think the reason why is a lack of foundation, which results in greatly decreased speed and accuracy.

I mean - do you ever write bad instead of bat ? Probably not. And if you think about it now you realise that 12x^2 is a completely different thing to 12x ? (assuming x > 1 or whatever).

These mistakes are mainly born out of a lack of real familiarity with manipulation in general.

Like working (x + 1)(x + 2) out as x^2 + 3x + 3 or something along those lines.

And imo this kind of thing just needs practice practice practice drill drill drill... this speed and accuracy problem. We all like to try and understand things rather than pattern match and that certainly should be the goal ( and requirement if you're thinking about teaching ) but to cut out these type of mistakes you probably just need to do a shed load of them until it's unthinkable to do them incorrectly.

This is what i was referring to when I said you'd be doing everything at once as well. You might not think you're having to learn that 12x is not equal to 12x^2 but a part of you needs to learn this kind of thing as you're making mistakes on it! Unforgivable mistakes (that I've made and make many of myself!).

So maybe it would be good to do a stock take - for arithmetic go through something like this perhaps - you should be able to shoot through them pretty quickly if your arithmetic is alright.

For the basic algebra maybe this would be suitable to go through. It doesn't teach you anything but there are a tonne of problems and you should be able to get through all of them pretty easily as well (or maybe not all but if you did the even numbered problems or something). There's an Algebra II book as well that might be worth going through in the same sense (you can find it on libgen or whatnot).

And this still hasn't covered any geometry, trig etc that comes before calc >.<.

Which is why I feel that it's hard, and that not everyone can do it because of physical time constraints as much as anything else.

[Precalculus with Limits 1e] (https://www.amazon.com/Precalculus-Limits-Ron-Larson/dp/0618660895/ref=sr_1_4?ie=UTF8&qid=1527656177&sr=8-4&keywords=larson+precalculus+with+limits) is a great book.

Beyond comprehensive coverage of the various types of functions (including logarithms and exponentials), trigonometry, and an introduction to complex numbers, the book covers [limits] (http://prntscr.com/jodi0c) and has a brief intro to [vectors] (http://prntscr.com/jodi3z), 3D space, the dot product, and cross product.

That is true, and for students who need to review the necessary algebra and trigonometry while they are taking calculus, I really like the book Just-in-Time Algebra & Trigonometry for Calculus by Guntram Mueller and Ronald Brent:

http://www.amazon.com/Just-Algebra-Trigonometry-Calculus-Edition/dp/032167104X

Here, all you need is to read this. I'm pretty sure you can get a pdf online.

The coveted TOPS green

Pick up pretty much any book on introductory analysis. I like this one. It will probably be more than you'll need, but it's only $10.

I vouch for Patrick JMT on youtube as well, although its more or less just a review of a small portion of what will be required calculus is all about practicing problems first hand, the textbook I currently use is full of them.
http://www.amazon.com/Calculus-Transcendentals-Soo-T-Tan/dp/0534465544

I have Thomas Calculus: 12th Edition if you'd like it.

Check around for a used copy, I picked up a used copy of Stewart 7th edition at the beginning of this semester off amazon for ~30 bucks.

Edit: try the used version here

http://www.amazon.com/Single-Variable-Calculus-Early-Transcendentals/dp/0538498676/ref=sr_1_2

https://www.amazon.com/Single-Variable-Calculus-Early-Transcendentals/dp/B006R9HHRM (The used copy)

https://www.amazon.com/Complete-Solutions-Stewarts-Variable-Transcendentals/dp/B00J4FLJ9S (The used copy as well)

If you can sing you could to a cover of this video.

Edit: or you could get the album I suppose

If you can find a copy somewhere cheap.

http://www.amazon.com/Calculus-Transcendentals-Available-Titles-CourseMate/dp/0534465544

Also, check out your library to see what other calculus books they might have.

Here is the mobile version of your link

This is the book

https://www.amazon.com/Calculus-Early-Transcendentals-Howard-Anton-ebook/dp/B01DV7OEI2


Okay, it's only asking for part A of the problem, I was about to do it by graphing it out, but even then I won't really know where it wants to be integrated from looking at the graph.

here, #33

"Humongous Book of Calculus" explains in english without treating you like a dummy or a 5 year old in need of a story.