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Cover of Calculus Volume 1

Calculus Volume 1

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 1 covers functions, limits, derivatives, and integration. 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 1 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-1. Changes: converted to CuraCourse lessons, with interactive practice added.

Table of contents

61 pages in 8 modules. Sign up to read and adopt them.

  1. Preface1 page
    1. Preface
  2. 1Functions and Graphs7 pages
    1. Introduction
    2. 1.1Review of Functions
    3. 1.2Basic Classes of Functions
    4. 1.3Trigonometric Functions
    5. 1.4Inverse Functions
    6. 1.5Exponential and Logarithmic Functions
    7. Practice
  3. 2Limits7 pages
    1. Introduction
    2. 2.1A Preview of Calculus
    3. 2.2The Limit of a Function
    4. 2.3The Limit Laws
    5. 2.4Continuity
    6. 2.5The Precise Definition of a Limit
    7. Practice
  4. 3Derivatives11 pages
    1. Introduction
    2. 3.1Defining the Derivative
    3. 3.2The Derivative as a Function
    4. 3.3Differentiation Rules
    5. 3.4Derivatives as Rates of Change
    6. 3.5Derivatives of Trigonometric Functions
    7. 3.6The Chain Rule
    8. 3.7Derivatives of Inverse Functions
    9. 3.8Implicit Differentiation
    10. 3.9Derivatives of Exponential and Logarithmic Functions
    11. Practice
  5. 4Applications of Derivatives12 pages
    1. Introduction
    2. 4.1Related Rates
    3. 4.2Linear Approximations and Differentials
    4. 4.3Maxima and Minima
    5. 4.4The Mean Value Theorem
    6. 4.5Derivatives and the Shape of a Graph
    7. 4.6Limits at Infinity and Asymptotes
    8. 4.7Applied Optimization Problems
    9. 4.8L’Hôpital’s Rule
    10. 4.9Newton’s Method
    11. 4.10Antiderivatives
    12. Practice
  6. 5Integration9 pages
    1. Introduction
    2. 5.1Approximating Areas
    3. 5.2The Definite Integral
    4. 5.3The Fundamental Theorem of Calculus
    5. 5.4Integration Formulas and the Net Change Theorem
    6. 5.5Substitution
    7. 5.6Integrals Involving Exponential and Logarithmic Functions
    8. 5.7Integrals Resulting in Inverse Trigonometric Functions
    9. Practice
  7. 6Applications of Integration11 pages
    1. Introduction
    2. 6.1Areas between Curves
    3. 6.2Determining Volumes by Slicing
    4. 6.3Volumes of Revolution: Cylindrical Shells
    5. 6.4Arc Length of a Curve and Surface Area
    6. 6.5Physical Applications
    7. 6.6Moments and Centers of Mass
    8. 6.7Integrals, Exponential Functions, and Logarithms
    9. 6.8Exponential Growth and Decay
    10. 6.9Calculus of the Hyperbolic Functions
    11. Practice
  8. Appendices3 pages
    1. ATable of Integrals
    2. BTable of Derivatives
    3. CReview of Pre-Calculus