## AP Calculus BC

### AP Calculus BC

Course Dates:
July 15-26
Course Pricing:
• \$810
Course Logistics:
Duration: 180 minutes (3 hours)
Number of Classes : 10 Classes
Occurs: Weekdays (1:30pm-4:30pm)
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### 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/Derivatives

• Limit and Derivative Rules (multiplication/division)
• Continuity, Limits with infinity, L'Hôpital's Rule
• Derivatives of Trigonometric and Exponential/Logarithmic Functions
• The Chain Rule, Related Rates, Higher Order Derivatives
• Implicit and Logarithmic Differentiation

### 02 - Evaluating Integrals

• Riemann Sums
• Integration by Substitution, Trigonometric Substitutions
• Integration by Parts
• Partial Fraction Decomposition
• Improper Integrals and Definite Integral Manipulations

### 03 - Applications of Integration

• Average Value of a function, Mean Value Theorem, Intermediate Value Theorem
• Areas of Bounded Regions
• Solids of Revolution, Solids with Cross Sections
• Arc Length
• Moment of Inertia

### 04 - Differential Equations

• Introducing Differential Equations
• Euler's Method of Approximations and Slope Fields
• Solving Separable Differential Equations
• Logistic and Exponential Functions
• Modeling / Population Growth

### 05 - Parametric and Polar

• Derivatives of Parametric and Vector Valued Functions
• Accumulation of Change with Definite Integrals, Integration to find position of a particle
• Speed, Velocity Vectors, and Acceleration Vectors of a particle
• Derivatives of Polar Functions, Introduction to finding areas bounded by polar functions
• Areas of regions bounded by polar curves

### 06 - Sequences and Series

• Definition of Convergence, Absolute Convergence, Conditional Convergence with Limits
• Basis types of series (Geometric, Harmonic, p-series), Convergence and Divergence tests
• Alternating Series Error Bound, Approximating convergent series
• Introduction to Taylor and Maclaurin Series, Interval and radius of convergence
• Taylor's  Theorem, Lagrange Error Bound, Calculating and Manipulating power series with derivatives and integrals