#### Holiday Announcement

In observance of Cesar Chavez Day, UC Scout will be closed on Friday, March 31, 2023. We will resume normal business hours on Monday, April 3, 2023.

# 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**: 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 0: Review**

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

**Unit 1: Limits and Continuity**

- Finding Limits Graphically and Numerically
- Evaluating Limits Analytically
- One-sided Limits
- Continuity and Intermediate Value Theorem
- Infinite Limits
- Limits at Infinity

**Unit 2: Differentiation Definition and Fundamental Properties**

- The Derivative and the Tangent Line Problem
- Basic Differentiation Rules
- Equations of a tangent Line
- The Natural Logarithmic Functions: Differentiation
- The Product and Quotient Rules

**Unit 3: Differentiation: Composite, Implicit and Inverse Functions**

- The Chain Rule
- Implicit Differentiation
- Inverse Functions
- Inverse Trigonometric Functions and Differentiation

**Unit 4: Contextual Applications of Differentiation**

- Velocity and Acceleration
- Related Rates - Introduction
- Related Rates - Advanced Examples
- Indeterminate Forms and L'Hopital's Rule

## SEMESTER 2

**Unit 5: Analytical Applications of Differentiation**

- Rolle's Theorem
- The Mean Value Theorem
- Extrema on an Interval
- Extrema on a Closed Interval
- Increasing and Decreasing Functions and the First Derivative Test
- Concavity and the Second Derivative Test
- A Summary of Curve Sketching
- Optimization Problems

**Unit 6: Integration and Accumulation of Change**

- Left and Right Side Approximations
- Area - Midpoint and Trapezoidal Approximations
- Riemann Sums and Definite Integrals
- Antidifferentiation and Indefinite Integration
- The Fundamental Theorem of Calculus
- Integration by Substitution
- The Natural Logarithmic Functions: Integration
- Exponential Functions: Differentiation and Integration
- Bases Other Than e and Applications
- Inverse Trigonometric Functions and Integration
- Trigonometric Integrals
- Trigonometric Substitution

**Unit 7: Differential Equations**

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

**Unit 8: Applications of Integration**

- Area of a Region Between Two Curves
- Area of a Region Between Two Curves - Advanced Examples
- Volume: Solids with Known Cross Sections
- Volume: The Disk Method
- Volume: The Shell Method