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Cover of Calculus Volume 2

Calculus Volume 2

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 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates. 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 2 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-2. 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. 1Integration9 pages
    1. Introduction
    2. 1.1Approximating Areas
    3. 1.2The Definite Integral
    4. 1.3The Fundamental Theorem of Calculus
    5. 1.4Integration Formulas and the Net Change Theorem
    6. 1.5Substitution
    7. 1.6Integrals Involving Exponential and Logarithmic Functions
    8. 1.7Integrals Resulting in Inverse Trigonometric Functions
    9. Practice
  3. 2Applications of Integration11 pages
    1. Introduction
    2. 2.1Areas between Curves
    3. 2.2Determining Volumes by Slicing
    4. 2.3Volumes of Revolution: Cylindrical Shells
    5. 2.4Arc Length of a Curve and Surface Area
    6. 2.5Physical Applications
    7. 2.6Moments and Centers of Mass
    8. 2.7Integrals, Exponential Functions, and Logarithms
    9. 2.8Exponential Growth and Decay
    10. 2.9Calculus of the Hyperbolic Functions
    11. Practice
  4. 3Techniques of Integration9 pages
    1. Introduction
    2. 3.1Integration by Parts
    3. 3.2Trigonometric Integrals
    4. 3.3Trigonometric Substitution
    5. 3.4Partial Fractions
    6. 3.5Other Strategies for Integration
    7. 3.6Numerical Integration
    8. 3.7Improper Integrals
    9. Practice
  5. 4Introduction to Differential Equations7 pages
    1. Introduction
    2. 4.1Basics of Differential Equations
    3. 4.2Direction Fields and Numerical Methods
    4. 4.3Separable Equations
    5. 4.4The Logistic Equation
    6. 4.5First-Order Linear Equations
    7. Practice
  6. 5Sequences and Series8 pages
    1. Introduction
    2. 5.1Sequences
    3. 5.2Infinite Series
    4. 5.3The Divergence and Integral Tests
    5. 5.4Comparison Tests
    6. 5.5Alternating Series
    7. 5.6Ratio and Root Tests
    8. Practice
  7. 6Power Series6 pages
    1. Introduction
    2. 6.1Power Series and Functions
    3. 6.2Properties of Power Series
    4. 6.3Taylor and Maclaurin Series
    5. 6.4Working with Taylor Series
    6. Practice
  8. 7Parametric Equations and Polar Coordinates7 pages
    1. Introduction
    2. 7.1Parametric Equations
    3. 7.2Calculus of Parametric Curves
    4. 7.3Polar Coordinates
    5. 7.4Area and Arc Length in Polar Coordinates
    6. 7.5Conic Sections
    7. Practice
  9. Appendices3 pages
    1. ATable of Integrals
    2. BTable of Derivatives
    3. CReview of Pre-Calculus