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OpenStax Calculus 1

Study guide for Calculus Volume 1 (Gilbert Strang, 2016 edition)

A study guide for OpenStax Calculus Volume 1 by Gilbert Strang and Edwin Herman, covering every section with practice problems and quizzes.

Independent study guide. Not affiliated with OpenStax or Rice University.

Chapter 1: Functions and Graphs

  1. 1.1Review of Functions
  2. 1.2Basic Classes of Functions
  3. 1.3Trigonometric Functions
  4. 1.4Inverse Functions
  5. 1.5Exponential and Logarithmic Functions

Chapter 2: Limits

  1. 2.1A Preview of Calculus
  2. 2.2The Limit of a Function
  3. 2.3The Limit Laws
  4. 2.4Continuity
  5. 2.5The Precise Definition of a Limit

Chapter 3: Derivatives

  1. 3.1Defining the Derivative
  2. 3.2The Derivative as a Function
  3. 3.3Differentiation Rules
  4. 3.4Derivatives as Rates of Change
  5. 3.5Derivatives of Trigonometric Functions
  6. 3.6The Chain Rule
  7. 3.7Derivatives of Inverse Functions
  8. 3.8Implicit Differentiation
  9. 3.9Derivatives of Exponential and Logarithmic Functions

Chapter 4: Applications of Derivatives

  1. 4.1Related Rates
  2. 4.2Linear Approximations and Differentials
  3. 4.3Maxima and Minima
  4. 4.4The Mean Value Theorem
  5. 4.5Derivatives and the Shape of a Graph
  6. 4.6Limits at Infinity and Asymptotes
  7. 4.7Applied Optimization Problems
  8. 4.8L'Hopital's Rule
  9. 4.9Newton's Method
  10. 4.10Antiderivatives

Chapter 5: Integration

  1. 5.1Approximating Areas
  2. 5.2The Definite Integral
  3. 5.3The Fundamental Theorem of Calculus
  4. 5.4Integration Formulas and the Net Change Theorem
  5. 5.5Substitution
  6. 5.6Integrals Involving Exponential and Logarithmic Functions
  7. 5.7Integrals Resulting in Inverse Trigonometric Functions

Chapter 6: Applications of Integration

  1. 6.1Areas between Curves
  2. 6.2Determining Volumes by Slicing
  3. 6.3Volumes of Revolution: Cylindrical Shells
  4. 6.4Arc Length of a Curve and Surface Area
  5. 6.5Physical Applications
  6. 6.6Moments and Centers of Mass
  7. 6.7Integrals, Exponential Functions, and Logarithms
  8. 6.8Exponential Growth and Decay
  9. 6.9Calculus of the Hyperbolic Functions