**by Don Shimamoto**

DescriptionTable of ContentsDetailsHashtagsReport an issue ### Book Description

This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking, the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and, finally, the general case of vector-valued functions of many variables. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. Otherwise, the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful, but not required. ### Table of Contents

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This open book is licensed under a Creative Commons License (CC BY). You can download Multivariable Calculus ebook for free in PDF format (12.9 MB).

Chapter 1

Rn

Chapter 2

Paths and curves

Chapter 3

Real-valued functions: preliminaries

Chapter 4

Real-valued functions: differentiation

Chapter 5

Real-valued functions: integration

Chapter 6

Differentiability and the chain rule

Chapter 7

Change of variables

Chapter 8

Vector fields

Chapter 9

Line integrals

Chapter 10

Surface integrals

Chapter 11

Working with differential forms

Subject

Mathematics

Publisher

Self-publishing

Published

2019

Pages

326

Edition

1

Language

English

ISBN13 Digital

9781708246990

ISBN10 Digital

1708246991

PDF Size

12.9 MB

License

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