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  • Differential Calculus - Chapter 1 -Rates of Change and the Derivative
    • Preface
    • 1 - Average Rates of Change
    • 2 - Prelude to Instantaneous Rates of Change
    • 3 - Limits and Continuity
    • 4 - Instantaneous Rates of Change: The Derivative
    • 5 - Extrema and the Mean Value Theorem
    • 6 - Higher-Order Derivatives
  • Chapter 2 - Basic Rules for Calculating Derivatives
    • 1 - The Power Rule for Integer Powers
    • 2 - The Product and Quotient Rules
    • 3 - The Chain Rule
    • 4 - The Exponential Function
    • 5 - The Natural Logarithm
    • 6 - General Exponential and Logarithmic Functions
    • 7 - Trigonometric Functions: Sine and Cosine
    • 8 - The Other Trigonometric Functions
    • 9 - Inverse Trig Functions
    • 10 - Implicitly Defined Functions
  • Chapter 3 - Applications of Differentiation
    • 1 - Related Rates
    • 2 - Graphing
    • 3 - Optimization
    • 4 - Linear Approximation, Differentials, and Newton’s Method
    • 5 - Indeterminate Forms and L´Hôpital’s Rule
  • Chapter 4 - Introduction to Differential Equations
    • 1 - What is a Differential Equation?
    • 2 - Anti-Derivatives
    • 3 - Separable Differential Equations
    • 4 - Applications of Differential Equations
    • 5 - Approximating Solutions of y'=m(x,y)
    • Appendix
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