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Mathematics LibreTexts

UCD Mat 21A: Differential Calculus

1. Functions

  • 1.1 Functions and Their Graphs
  • 1.2 Combining Functions; Shifting and Scaling Graphs
  • 1.3 Trigonometric Functions
  • 1.4 Graphing with Calculators and Computers
  • 1.5 Exponential Functions
  • 1.6 Inverse Functions and Logarithms

2. Limits and Derivatives

  • 2.1 Rates of Change and Tangents to Curves
  • 2.2 Limit of a Function and Limit Laws
  • 2.3 Precise Definition of a Limit
  • 2.4 One-Sided Limits
  • 2.5 Continuity
  • 2.6 Limits Involving Infinity, Asymptotes of Graphs

3. Differentiation

  • 3.1 Tangents and the Derivative at a Point
  • 3.2 The Derivative as a Function
  • 3.3 Rules for Polynomials, Exponentials, Products, and Quotients
  • 3.4 The Derivative as a Rate of Change
  • 3.5 Derivatives of Trigonometric Functions
  • 3.6 The Chain Rule
  • 3.7 Implicit Differentiation
  • 3.8 Derivatives of Inverse Functions and Logarithms
  • 3.9 Inverse Trigonometric Functions
  • 3.10 Related Rates
  • 3.11 Linearization and Differentials

4. Applications of Derivatives

  • 4.1 Extreme Values of Functions
  • 4.2 The Mean Value Theorem
  • 4.3 Monotonic Functions and the First Derivative Test
  • 4.4 Concavity and Curve Sketching
  • 4.5 Indeterminate Forms and L'Hopital's Rule
  • 4.6 Applied Optimization
  • 4.7 Newton's Method
  • 4.8 Antiderivatives