**Pre-Requisites:** Algebra I, Geometry, Algebra II, Pre-Calculus or Trigonometry/Analytical Geometry.

**Credits:** 1.0

**Estimated Completion Time:** 32-36 weeks

__Segment One__

Module 01 - Limits and Continuity

- Using Limits to Analyze Instantaneous Change
- Estimating Limit Values from Graphs and Tables
- Determining Limits Using Algebraic Properties and Manipulation
- Selecting Procedures for Determining Limits
- Squeeze Theorem and Representations of Limits
- Determining Continuity and Exploring Discontinuity
- Connecting Limits, Infinity, and Asymptotes
- The Intermediate Value Theorem (IVT)

Module 02 - Differentiation: Definition and Fundamental Properties

- Average and Instantaneous Rates of Change and the Derivative Definition
- Determining Differentiability and Estimating Derivatives
- Derivative Rules: Constant, Sum, Difference, Constant Multiple, and Power
- The Product Rule and the Quotient Rule
- Derivatives of Trigonometric Functions
- Derivatives of Exponential and Logarithmic Functions

Module 03 - Differentiation: Composite, Implicit, and Inverse Functions

- The Chain Rule
- Implicit Differentiation
- Differentiating Inverse Functions
- Differentiating Inverse Trigonometric Functions
- Selecting Procedures for Calculating Derivatives
- Calculating Higher-Order Derivatives

Module 04 - Contextual Applications of Differentiation

- Interpreting and Applying the Derivative in Motion
- Rates of Change in Applied Contexts Other Than Motion
- Related Rates
- Approximating Values of a Function Using Local Linearity and Linearization
- L'Hospital's Rule

Module 05 - Analytical Applications of Differentiation

- Mean Value and Extreme Value Theorems
- Determining Function Behavior and the First Derivative Test
- Using the Candidates Test to Determine Absolute Extrema
- Determining Concavity of Functions and the Second Derivative Test
- Connecting Graphs of Functions and Their Derivatives
- Optimization Problems
- Exploring Behaviors of Implicit Relations

__Segment Two__

Module 06 - Integration and Accumulation of Change

- Exploring Accumulations of Change
- Riemann Sums and the Definite Integral
- Accumulation Functions Involving Area and the Fundamental Theorem of Calculus
- Applying Properties of Definite Integrals
- Finding Antiderivatives and Indefinite Integrals
- Integrating Using Substitution
- Integrating Using Integration by Parts
- Integrating Using Linear Partial Fractions
- Evaluating Improper Integrals
- Integrating Functions Using Long Division and Completing the Square
- Selecting Techniques for Antidifferentiation

Module 07 - Differential Equations

- Solutions of Differential Equations
- Sketching and Reasoning Using Slope Fields
- Approximating Solutions Using Euler's Method
- Finding Solutions Using Separation of Variables
- Exponential Models with Differential Equations
- Logistic Models with Differential Equations

Module 08 - Applications of Integration

- Average Value and Connecting Position, Velocity, and Acceleration Using Integrals
- Using Accumulation Functions and Definite Integrals in Applied Contexts
- Finding the Area Between Curves
- Finding the Area Between Curves That Intersect at More Than Two Points
- Volumes with Discs
- Volumes with Washers
- Volumes with Cross Sections
- The Arc Length of a Smooth, Planar Curve and Distance Traveled

Module 09 - Parametric, Polar, and Vector-Valued Equations

- Differentiating Parametric Equations and Finding Arc Length
- Differentiating and Integrating Vector-Valued Functions
- Solving Motion Problems Using Parametric and Vector-Valued Functions
- Defining Polar Coordinates and Differentiating in Polar Form
- Finding Area Bounded by Polar Curves

Module 10 - Infinite Sequences and Series

- Convergent and Divergent Infinite Series and Geometric Series
- Integral Test for Convergence, Harmonic Series, and p-Series
- Comparison Tests for Convergence
- Additional Tests to Determine Convergence
- Alternating Series and Their Error Bound
- Taylor Polynomial Approximations of Functions and Evaluating Error
- Radius and Interval of Convergence of Power Series
- Finding Taylor or Maclaurin Series for a Function
- Representing Functions as Power Series

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