
# 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