By Jerrold Marsden, Alan Weinstein

The 3rd of a three-volume paintings, this e-book is the outgrowth of the authors' event instructing calculus at Berkeley. It covers multivariable calculus and starts off with the mandatory fabric from analytical geometry. It is going directly to conceal partial differention, the gradient and its purposes, a number of integration, and the theorems of eco-friendly, Gauss and Stokes. The authors inspire the learn of calculus utilizing its purposes. good points many solved difficulties and vast routines.

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**Extra info for Calculus III (Undergraduate Texts in Mathematics)**

**Sample text**

That’s absurd! It seems crazy, just like negatives, zero, and irrationals (non-repeating numbers) must have seemed crazy at first. There’s no “real” meaning to this question, right? Wrong. So-called “imaginary numbers” are as normal as every other number (or just as fake): they’re a tool to describe the world. 3, and 0 “exist”, let’s assume some number i exists where: That is, you multiply i by itself to get -1. What happens now? Well, first we get a headache. New relationships emerge that we can describe with ease.

And if you don’t, well, I’m afraid math doesn’t toot your horn. Sorry. Trigonometry is great, but complex numbers can make ugly calculations simple (like calculating cosine(a+b) ). This is just a preview; later articles will give you the full meal. Complex Numbers Aren’t That was a whirlwind tour of my basic insights. Take a look at the first chart — it should Math, Better Explained 6 Imaginary Numbers 58 of 144 make sense now. There’s so much more to these beautiful, zany numbers, but my brain is tired.

We’ll approach imaginary numbers by observing its ancestor, the negatives. Here’s your guidebook: Math, Better Explained 6 Imaginary Numbers 43 of 144 It doesn’t make sense yet, but hang in there. By the end we’ll hunt down i and put it in a headlock, instead of the reverse. Really Understanding Negative Numbers Negative numbers aren’t easy. Imagine you’re a European mathematician in the 1700s. You have 3 and 4, and know you can write 4 - 3 = 1. Simple. But what about 3-4? What, exactly, does that mean?