Worldwide multivariable Calculus

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David B. Massey– Northeastern University

ISBN-10: 0-9842071-3-9
ISBN-13: 978-0-9842071-3-8
605 Pages
©2019 Worldwide Center of Mathematics, LLC

Digital | $19.95
Print | $39.95 + shipping

 

Features

 

contents

 

Supplements

Introduction

Multivariable Calculus is the study of the Calculus of functions of more than one variable, and includes differential and integral aspects. This book is written by David B. Massey, Ph.D., an award-winning teacher and world-renowned research mathematician, who has been teaching college students for 30 years. He emphasizes intuitive ideas in conjunction with rigorous statements of theorems, and provides a large number of illustrative examples. In the accompanying videos, Dr. Massey lectures on the core material from each section.


Features

  • Written by an award-winning mathematics professor with 30 years of teaching experience
  • Down-to-Earth exposition
  • Completely rigorous definitions, statements of theorems, and illustrative proofs
  • External references to more-technical proofs
  • Sections are divided into Basics, More Depth, and, where appropriate, +Linear Algebra
  • Margin side-remarks and historical references
  • Hyperlinked table of contents, index, and cross-references
  • Hyperlinks are provided to Wikipedia content on linear algebra
  • Embedded video links to full-length lectures
  • Video-solutions to select exercises
  • PDF format, compatible with all computers, tablets, and mobile devices
  • Low cost in electronic or print form

Contents

  • 1.1 Euclidean Space
  • 1.1.1 Exercises
  • 1.2 Rn as a Vector Space
  • 1.2.1 Exercises
  • 1.3 Dot Product, Angles & Projection
  • 1.3.1 Exercises
  • 1.4 Lines, Planes, and Hyperplanes
  • 1.4.1 Exercises
  • 1.5 The Cross Product
  • 1.5.1 Exercises
  • 1.6 Functions of a Single Variable
  • 1.6.1 Exercises
  • 1.7 Multivariable Functions
  • 1.7.1 Exercises
  • 1.8 Graphing Surfaces
  • 1.8.1 Exercises
  • 2.1 Partial Derivatives
  • 2.1.1 Exercises
  • 2.2 The Total Derivative
  • 2.2.1 Exercises
  • 2.3 Linear Approximation, Tangent Planes, and the Differential
  • 2.3.1 Exercises
  • 2.4 Differentiation Rules
  • 2.4.1 Exercises
  • 2.5 The Directional Derivative
  • 2.5.1 Exercises
  • 2.6 Change of Coordinates
  • 2.6.1 Exercises
  • 2.7 Level Sets & Gradient Vectors
  • 2.7.1 Exercises
  • 2.8 Parameterizing Surfaces
  • 2.8.1 Exercises
  • 2.9 Local Extrema
  • 2.9.1 Exercises
  • 2.10 Optimization
  • 2.10.1 Exercises
  • 2.11 Lagrange Multipliers
  • 2.11.1 Exercises
  • 2.12 Implicit Differentiation
  • 2.12.1 Exercises
  • 2.13 Multivariable Taylor Polynomials & Series
  • 2.13.1 Exercises
  • 3.1 Iterated Integrals
  • 3.1.1 Exercises
  • 3.2 Integration in R2
  • 3.2.1 Exercises
  • 3.3 Polar Coordinates
  • 3.3.1 Exercises
  • 3.4 Integration in R3 and Rn
  • 3.4.1 Exercises
  • 3.5 Volume
  • 3.5.1 Exercises
  • 3.6 Cylindrical and Spherical Coordinates
  • 3.6.1 Exercises
  • 3.7 Average Value
  • 3.7.1 Exercises
  • 3.8 Density & Mass
  • 3.8.1 Exercises
  • 3.9 Centers of Mass
  • 3.9.1 Exercises
  • 3.10 Moments of Inertia
  • 3.10.1 Exercises
  • 3.11 Surfaces and Area
  • 3.11.1 Exercises
  • 4.1 Vector Fields
  • 4.1.1 Exercises
  • 4.2 Line Integrals
  • 4.2.1 Exercises
  • 4.3 Conservative Vector Fields
  • 4.3.1 Exercises
  • 4.4 Green's Theorem
  • 4.4.1 Exercises
  • 4.5 Flux through a Surface
  • 4.5.1 Exercises
  • 4.6 The Divergence Theorem
  • 4.6.1 Exercises
  • 4.7 Stokes' Theorem
  • 4.7.1 Exercises

 

 

Supplements

 

Worldwide Multivariable Calculus Solution Manual (faculty) go >
Faculty may request the available free faculty digital resources online.

Worldwide Multivariable Calculus Study Guide ($4.95) go>

Worldwide Multivariable Calculus Video Playlist (Free) go >
Worldwide Multivariable Calculus features associated video selections made available free on the Center of Math YouTube Channel. Video links are directly embedded in the digital textbook.

WebAssign go >
Worldwide Multivariable Calculus is available with WebAssign. WebAssign is a powerful digital solution designed by educators to enrich the teaching and learning experience. WebAssign provides extensive content, instant assessment, and superior support.