# AP Calculus AB

What do electrical engineers, economists, and business managers have in common? All use calculus to answer big questions on the job. In this course, you’ll explore the basics of calculus including functions, graphs, integrals, and more, all while gaining valuable problem solving skills. RECOMMENDED PREREQUISITE: Successful completion of math through Algebra II, Math III and/or Pre-Calculus equivalent.

Basic and On Demand are always open for registration.

Plus courses are created upon request.

## SEMESTER 1

**Unit 1: Review**

- Lines
- Functions and Graphs
- Exponential Functions
- Functions and Logarithms
- Trigonometric Functions

**Unit 2: Limits**

- Finding Limits Graphically and Numerically
- Evaluating Limits Analytically
- One-sided Limits
- Continuity
- InfiniteLimits

**Unit 3: Derivatives**

- The Derivative and the Tangent Line Problem
- Basic Differentiation Rules
- Product and Quotient Rules
- Equations of a Tangent Line
- Velocity and Acceleration
- The Chain Rule
- Implicit Differentiation
- Related Rates - Introduction
- Related Rates - Advanced Examples

**Unit 4: Application of Derivatives**

- Extrema on an Interval
- Extrema on a Closed Interval
- Rolle’s Theorem
- Mean Value Theorem
- Increasing and Decreasing Functions and the First Derivative Test
- Concavity and the Second Derivative Test
- Limits at Infinity
- A Summary of Curve Sketching
- Optimization Problems
- Indeterminate Forms and L’Hospital’s Rule

## SEMESTER 2

**Unit 5: Integration**

- Antiderivatives and Indefinite Integration
- Area - Left and Right Side Approximations
- Area - Midpoint and Trapezoidal Approximations
- Riemann Sums and Definite Integrals
- The Fundamental Theorem of Calculus
- Integration by Substitution

**Unit 6: Advanced Functions**

- The Natural Logarithmic Functions: Differentiation
- The Natural Logarithmic Functions: Integration
- Inverse Functions
- Exponential Functions: Differentiation and Integration
- Bases Other Than e and Applications
- Inverse Trigonometric Functions and Differentiation
- Inverse Trigonometric Functions and Integration

**Unit 7: Application of Integration**

- Slope Fields
- Separation of Variables
- Differential Equations: Growth and Decay

**Unit 8: Area, Volume, and Work**

- Area of a Region Between Two Curves
- Area of a Region Between Two Curves - Advanced Examples
- Volume: The Disc Method
- Solids with Known Cross-sections
- Volume: The Shell Method
- Work