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Want a future in video game engineering, economics, or science? Then this AP Calculus course is for you. Calculus is the mathematical study of change. After taking this course youâ€™ll be able to work with functions in a variety of ways, and be able to use derivatives to solve a variety of problems, which is math-speak for having the skills to build the future of technology. This course features a wide range of readings, simulations, assessments, and more to ensure successful course completion.

Unit 0: Review

- Lines
- Functions and Graphs
- Exponential Functions
- Functions and Logarithms
- TTrigonometric Functions

UUnit 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

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 Part 1: 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

Unit 6 Part 2: More Integration Techniques

- Exponential Functions: Differentiation and Integration
- Bases Other Than e and Applications
- Inverse Trigonometric Functions and Integration
- Trigonometric Integrals
- Trigonometric Substitution
- Integration by Parts (BC Only)
- Partial Fractions (BC Only)
- Improper Integrals (BC Only)

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
- Arc Length (BC Only)

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC Only)

- Parametric Equations
- Differentiation of Parametric Equations
- Vector-Valued Functions
- Differentiation and Integration of Vector-Valued Functions
- Velocity and Acceleration Using Parametric and Vector Valued Functions
- Polar Coordinates and Polar Graphs
- Polar Form of a Derivative
- Areas in Polar Coordinates

Unit 10: Infinite Sequences and Series (BC Only)

- Sequences
- Infinite and Geometric Series
- The Integral Test and p-Series
- Comparisons of Series and the Ratio Test
- Alternating Series
- Taylor Polynomials and Approximations
- Power Series
- Taylor and Maclaurin Series
- Representation of Functions by Power Series

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