Calculus Volume 1

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.

Senior Contributing Authors

Gilbert Strang, Massachusetts Institute of Technology
Edwin “Jed” Herman, University of Wisconsin-Stevens Point

Contributing Authors

Joseph Lakey, New Mexico State University
Elaine A. Terry, Saint Joseph’s University
Alfred K. Mulzet, Florida State College at Jacksonville
Sheri J. Boyd, Rollins College
Joyati Debnath, Winona State University
Michelle Merriweather, Bronxville High School
David Smith, University of the Virgin Islands
Nicoleta Virginia Bila, Fayetteville State University
Valeree Falduto, Palm Beach State College
Kirsten R. Messer, Colorado State University-Pueblo
William Radulovich, Formerly at Florida State College at Jacksonville
Erica M. Rutter, Arizona State University
David Torain, Hampton University
Catherine Abbott, Keuka College
Julie Levandosky, Framingham State University
David McCune, William Jewell College

Chapter 1 Functions and Graphs
• Introduction
• 1.1 Review of Functions
• 1.2 Basic Classes of Functions
• 1.3 Trigonometric Functions
• 1.4 Inverse Functions
• 1.5 Exponential and Logarithmic Functions
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
o Review Exercises

Chapter 2 Limits
• Introduction
• 2.1 A Preview of Calculus
• 2.2 The Limit of a Function
• 2.3 The Limit Laws
• 2.4 Continuity
• 2.5 The Precise Definition of a Limit
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
o Review Exercises

Chapter 3 Derivatives
• Introduction
• 3.1 Defining the Derivative
• 3.2 The Derivative as a Function
• 3.3 Differentiation Rules
• 3.4 Derivatives as Rates of Change
• 3.5 Derivatives of Trigonometric Functions
• 3.6 The Chain Rule
• 3.7 Derivatives of Inverse Functions
• 3.8 Implicit Differentiation
• 3.9 Derivatives of Exponential and Logarithmic Functions
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
o Review Exercises

Chapter 4 Applications of Derivatives
• Introduction
• 4.1 Related Rates
• 4.2 Linear Approximations and Differentials
• 4.3 Maxima and Minima
• 4.4 The Mean Value Theorem
• 4.5 Derivatives and the Shape of a Graph
• 4.6 Limits at Infinity and Asymptotes
• 4.7 Applied Optimization Problems
• 4.8 L’Hôpital’s Rule
• 4.9 Newton’s Method
• 4.10 Antiderivatives
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
o Review Exercises

Chapter 5 Integration
• Introduction
• 5.1 Approximating Areas
• 5.2 The Definite Integral
• 5.3 The Fundamental Theorem of Calculus
• 5.4 Integration Formulas and the Net Change Theorem
• 5.5 Substitution
• 5.6 Integrals Involving Exponential and Logarithmic Functions
• 5.7 Integrals Resulting in Inverse Trigonometric Functions
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
o Review Exercises

Chapter 6 Applications of Integration
• Introduction
• 6.1 Areas between Curves
• 6.2 Determining Volumes by Slicing
• 6.3 Volumes of Revolution: Cylindrical Shells
• 6.4 Arc Length of a Curve and Surface Area
• 6.5 Physical Applications
• 6.6 Moments and Centers of Mass
• 6.7 Integrals, Exponential Functions, and Logarithms
• 6.8 Exponential Growth and Decay
• 6.9 Calculus of the Hyperbolic Functions
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
o Review Exercises