## AP Calculus AB

### Summer Courses

### Advanced Courses

### AP Calculus AB

Grade Level:

Grade 9-12

Course Dates:

June 17, 2024 - July 12, 2024

Course Pricing:

$1620

Course Logistics:

Duration: 180 minutes (3 hours)

Number of Classes: 20 Classes

Occurs: Weekdays (1:30pm-4:30pm)

### Course Topics:

Course Topics are organized as six modules with five granular topics covered under each module. If a summer course offers sessions A and B, please note both sessions will cover the same content as described below. Click through below to see all modules/topics for this course.

### 01 - Limits & Continuity

- Introduction to the Idea of Limits
- Left and Right Hand Limits
- Limits involving Infinity
- The Squeeze Theorem
- Continuity

### 02 - Introduction to Differentiation

- Definitions and Notation
- Fundamental Derivative Rules (connecting these to the notion of derivatives of a limit)
- Derivatives of Logarithmic and Exponential Functions
- Derivatives of Trigonometric Functions
- Implicit Differentiation

### 03 - Applications of Derivatives

- Extrema, Graphing, Concavity
- Optimization (word problems)
- Approximations, Linearization, L'Hôpital's Rule
- Related Rates
- Mean / Intermediate Value Theorem

### 04 - Introduction to Integration

- Definition, notion of an integral
- Fundamental Theorem of Calculus - Statement and Intuition
- Applications of the Fundamental Theorem of Calculus
- Calculating Antiderivatives
- Various Riemann sums

### 05 - Methods of Integration

- U-Substitution
- Trigonometric Substitution
- Integration by Parts
- Partial Fraction Decomposition
- Improper Integrals

### 06 - Definite Integrals and Applications

- Definite Integral Manipulations and Simplifications
- Areas of Bounded Regions
- Volume of Solids and Revolutions
- Arc Length
- Moment of Inertia