Multivariable Calculus

by Don Shimamoto

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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.

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).

Table of Contents

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
 

Book Details

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
CC BY

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