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Cover of Calculus Volume 3

Calculus Volume 3

by Gilbert Strang and Edwin “Jed” Herman

Published by OpenStax

MathematicsCollege

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. Please note that this title is published under a CC BY-NC-SA 4.0 license, which means that you are free to use and adapt, but not for commercial purposes. Changes you make need to be shared using this license.

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Attribution

Adapted from Calculus Volume 3 by Gilbert Strang and Edwin “Jed” Herman, published by OpenStax (Rice University) under CC BY-NC-SA 4.0 (https://creativecommons.org/licenses/by-nc-sa/4.0/). Access the original for free at https://openstax.org/details/books/calculus-volume-3. Changes: converted to CuraCourse lessons, with interactive practice added.

Table of contents

61 pages in 9 modules. Sign up to read and adopt them.

  1. Preface1 page
    1. Preface
  2. 1Parametric Equations and Polar Coordinates7 pages
    1. Introduction
    2. 1.1Parametric Equations
    3. 1.2Calculus of Parametric Curves
    4. 1.3Polar Coordinates
    5. 1.4Area and Arc Length in Polar Coordinates
    6. 1.5Conic Sections
    7. Practice
  3. 2Vectors in Space9 pages
    1. Introduction
    2. 2.1Vectors in the Plane
    3. 2.2Vectors in Three Dimensions
    4. 2.3The Dot Product
    5. 2.4The Cross Product
    6. 2.5Equations of Lines and Planes in Space
    7. 2.6Quadric Surfaces
    8. 2.7Cylindrical and Spherical Coordinates
    9. Practice
  4. 3Vector-Valued Functions6 pages
    1. Introduction
    2. 3.1Vector-Valued Functions and Space Curves
    3. 3.2Calculus of Vector-Valued Functions
    4. 3.3Arc Length and Curvature
    5. 3.4Motion in Space
    6. Practice
  5. 4Differentiation of Functions of Several Variables10 pages
    1. Introduction
    2. 4.1Functions of Several Variables
    3. 4.2Limits and Continuity
    4. 4.3Partial Derivatives
    5. 4.4Tangent Planes and Linear Approximations
    6. 4.5The Chain Rule
    7. 4.6Directional Derivatives and the Gradient
    8. 4.7Maxima/Minima Problems
    9. 4.8Lagrange Multipliers
    10. Practice
  6. 5Multiple Integration9 pages
    1. Introduction
    2. 5.1Double Integrals over Rectangular Regions
    3. 5.2Double Integrals over General Regions
    4. 5.3Double Integrals in Polar Coordinates
    5. 5.4Triple Integrals
    6. 5.5Triple Integrals in Cylindrical and Spherical Coordinates
    7. 5.6Calculating Centers of Mass and Moments of Inertia
    8. 5.7Change of Variables in Multiple Integrals
    9. Practice
  7. 6Vector Calculus10 pages
    1. Introduction
    2. 6.1Vector Fields
    3. 6.2Line Integrals
    4. 6.3Conservative Vector Fields
    5. 6.4Green’s Theorem
    6. 6.5Divergence and Curl
    7. 6.6Surface Integrals
    8. 6.7Stokes’ Theorem
    9. 6.8The Divergence Theorem
    10. Practice
  8. 7Second-Order Differential Equations6 pages
    1. Introduction
    2. 7.1Second-Order Linear Equations
    3. 7.2Nonhomogeneous Linear Equations
    4. 7.3Applications
    5. 7.4Series Solutions of Differential Equations
    6. Practice
  9. Appendices3 pages
    1. ATable of Integrals
    2. BTable of Derivatives
    3. CReview of Pre-Calculus