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Multivariable Calculus

(1 review)

Don Shimamoto, Swarthmore College

Copyright Year: 2019

Last Update: 2020

Publisher: Don Shimamoto

Language: English

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Reviewed by Andy Rich, Professor of Mathematics, PALNI, Manchester University on 12/19/19

Has all the usual topics and then some. I liked the development of differential forms towards the end and having chapter 11 as a teaser for higher level stuff. The development was clear enough that I hope most students at this level could get... read more

Table of Contents

  • I Preliminaries
    • 1 Rn
  • II Vector-valued functions of one variable
    • 2 Paths and curves
  • III Real-valued functions
    • 3 Real-valued functions: preliminaries
    • 4 Real-valued functions: differentiation
    • 5 Real-valued functions: integration
  • IV Vector-valued functions
    • 6 Differentiability and the chain rule
    • 7 Change of variables
  • V Integrals of vector fields
    • 8 Vector fields
    • 9 Line integrals
    • 10 Surface integrals
    • 11 Working with differential forms

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About the Book

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.

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Don Shimamoto, Swarthmore College

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