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Chapters

Chapter 1: Analytic Geometry
  • This chapter is primarily a review of previous algebra and geometry concepts that you will need for calculus.
  • This chapter will NOT be covered in this course. I suggest reviewing this chapter as needed.
Chapter 2: Instantaneous Rate of Change: The Derivative
  • Notes
    • 2.3 Limits
    • 4.3 A Hard Limit
    • 2.4 The Derivative Function
    • 2.5 Adjectives for Functions
Chapter 3: Rules for Finding Derivatives
  • Notes
    • 3.1 The Power Rule
    • 3.2 Linearity of the Derivative
    • 3.3 The Product Rule
    • 3.4 The Quotient Rule
    • 3.5 The Chain Rule
Chapter 4: Transcendental Functions
  • Notes
    • 4.4 The Derivative of sin x
    • 4.5 Derivatives of the Trigonometric Functions
    • 4.6 Exponential and Logarithmic Functions
    • 4.7 Derivatives of Exponential and Logarithmic Functions
    • 4.8 Implicit Differentiation
    • 4.9 Inverse Trigonometric Functions
    • 4.10 Limits Revisited
    • 4.11 Hyperbolic Functions
Chapter 5: Curve Sketching
  • Notes
    • 5.1 Maxima and Minima
    • 5.2 The First Derivative Test
    • 5.3 The Second Derivative Test
    • 5.4 Concavity and Inflection Points
    • 5.5 Asymptotes and Other Things to Look For
Chapter 6: Applications of the Derivative
  • Notes
    • 6.1 Optimization
    • 6.2 Related Rates
    • 6.3 Newton’s Method
    • 6.4 Linear Approximations
    • 6.5 The Mean Value Theorem
Chapter 7: Integration
  • Notes
    • 7.1 Two Examples
    • 7.2 The Fundamental Theorem of Calculus
    • 7.3 Some Properties of Integrals

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