# 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