TITLE> Syllabus

# Syllabus

### Introduction to derivative

• Power, constant, sum rules (Chapter 1). Slope and tangent line (Chapter 2).
• Product, quotient rules ( Chapter 3).
• Chain rule (Chapter 4).
• Implicit diffentiation (Chapter 4).
• Extended power rule (Chapter 5).

### Differentiation of elementary functions

• Trigonometric review: triangles, trigonometric formulas (Chapter 6, two classes).
• Trigonometric review: periodic functions. Derivative of sin and cos (Chapter 6).
• exp and log basic properties. e as a limit. (Chapter 9).
• Derivatives of ex and ln x (Chapter 9).
• Exponential growth. Exponential decay. Rates of growth (Capter 10 and Chapter 7).

### Applications

• Max/Min problems (Chapter 7).
• Real-world problems (Chapter 8, two classes).
• Second derivative. Concavity. Acceleration (Chapter 11).
• Curve sketching (Chapter 11, two classes).

### Introduction to integral

• Antiderivatives. Differential equations (Chapter 12).
• Area. Definite integral (Chapter 15).