Read more about Calculus Volume 3

Calculus Volume 3

(2 reviews)

Gilbert Strang, Massachusetts Institute of Technology

Copyright Year: 2016

ISBN 13: 9781938168079

Publisher: OpenStax

Language: English

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Reviewed by Rob Niemeyer, Assistant Professor, Metropolitan State University of Denver on 10/21/19

The text is very comprehensive. All of the important topics are covered and the examples are very thorough. That said, I would have liked to see something on the higher-order derivative test. The reason for the '4' in this category is that... read more

Reviewed by Paul Meyer Reimer, Professor of Physics, Goshen College on 7/15/19

The first 6 chapters (of 7) cover what I currently cover in a Multivariable Calculus course. Well, actually a good deal more than I cover! I would go lightly on the conic sections material and several of the sections on physics applications... read more

Table of Contents

1. Parametric Equations and Polar Coordinates

  • 1.1. Introduction
  • 1.2. Parametric Equations
  • 1.3. Calculus of Parametric Curves
  • 1.4. Polar Coordinates
  • 1.5. Area and Arc Length in Polar Coordinates
  • 1.6. Conic Sections

2. Vectors in Space

  • 2.1. Introduction
  • 2.2. Vectors in the Plane
  • 2.3. Vectors in Three Dimensions
  • 2.4. The Dot Product
  • 2.5. The Cross Product
  • 2.6. Equations of Lines and Planes in Space
  • 2.7. Quadric Surfaces
  • 2.8. Cylindrical and Spherical Coordinates

3. Vector-Valued Functions

  • 3.1. Introduction
  • 3.2. Vector-Valued Functions and Space Curves
  • 3.3. Calculus of Vector-Valued Functions
  • 3.4. Arc Length and Curvature
  • 3.5. Motion in Space

4. Differentiation of Functions of Several Variables

  • 4.1. Introduction
  • 4.2. Functions of Several Variables
  • 4.3. Limits and Continuity
  • 4.4. Partial Derivatives
  • 4.5. Tangent Planes and Linear Approximations
  • 4.6. The Chain Rule
  • 4.7. Directional Derivatives and the Gradient
  • 4.8. Maxima/Minima Problems
  • 4.9. Lagrange Multipliers

5. Multiple Integration

  • 5.1. Introduction
  • 5.2. Double Integrals over Rectangular Regions
  • 5.3. Double Integrals over General Regions
  • 5.4. Double Integrals in Polar Coordinates
  • 5.5. Triple Integrals
  • 5.6. Triple Integrals in Cylindrical and Spherical Coordinates
  • 5.7. Calculating Centers of Mass and Moments of Inertia
  • 5.8. Change of Variables in Multiple Integrals

6. Vector Calculus

  • 6.1. Introduction
  • 6.2. Vector Fields
  • 6.3. Line Integrals
  • 6.4. Conservative Vector Fields
  • 6.5. Green's Theorem
  • 6.6. Divergence and Curl
  • 6.7. Surface Integrals
  • 6.8. Stokes' Theorem
  • 6.9. The Divergence Theorem

7. Second-Order Differential Equations

  • 7.1. Introduction
  • 7.2. Second-Order Linear Equations
  • 7.3. Nonhomogeneous Linear Equations
  • 7.4. Applications
  • 7.5. Series Solutions of Differential Equations

Table of IntegralsTable of DerivativesReview of Pre-Calculus

Ancillary Material

  • OpenStax
  • About the Book

    Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

    About the Contributors


    Gilbert Strang was an undergraduate at MIT and a Rhodes Scholar at Balliol College, Oxford. His Ph.D. was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. He is a Professor of Mathematics at MIT, an Honorary Fellow of Balliol College, and a member of the National Academy of Sciences. 

    He was the President of SIAM during 1999 and 2000, and Chair of the Joint Policy Board for Mathematics. He received the von Neumann Medal of the US Association for Computational Mechanics, and the Henrici Prize for applied analysis. The first Su Buchin Prize from the International Congress of Industrial and Applied Mathematics, and the Haimo Prize from the Mathematical Association of America, were awarded for his contributions to teaching around the world. 

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