Unit 1 Limits and Continuity

1. Topics 1.1–1.2 · 20 minIntroducing Calculus: Can Change Occur at an Instant? · Defining Limits and Using Limit Notation
2. Topics 1.3–1.4 · 19 minEstimating Limit Values from Graphs · Estimating Limit Values from Tables
3. Topics 1.5–1.6 · 24 minDetermining Limits Using Algebraic Properties of Limits · Determining Limits Using Algebraic Manipulation
4. Topics 1.7–1.9 · 20 minSelecting Procedures for Determining Limits · Determining Limits Using the Squeeze Theorem · Connecting Multiple Representations of Limits
5. Topics 1.10, 1.11, 1.13 · 19 minExploring Types of Discontinuities · Defining Continuity at a Point · Removing Discontinuities
6. Topics 1.12, 1.16 · 21 minConfirming Continuity over an Interval · Working with the Intermediate Value Theorem (IVT)
7. Topics 1.14–1.15 · 20 minConnecting Infinite Limits and Vertical Asymptotes · Connecting Limits at Infinity and Horizontal Asymptotes

Unit 2 Differentiation: Definition and Fundamental Properties

1. Topic 2.1 · 20 minDefining Average and Instantaneous Rates of Change at a Point
2. Topic 2.2 · 19 minDefining the Derivative of a Function and Using Derivative Notation
3. Topics 2.3–2.4 · 22 minEstimating Derivatives of a Function at a Point · Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
4. Topics 2.5–2.6 · 20 minApplying the Power Rule · Derivative Rules: Constant, Sum, Difference, and Constant Multiple
5. Topic 2.7 · 21 minDerivatives of cos x, sin x, e^x, and ln x
6. Topics 2.8–2.10 · 23 minThe Product Rule · The Quotient Rule · Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

Unit 3 Differentiation: Composite, Implicit, and Inverse Functions

1. Topic 3.1 · 21 minThe Chain Rule
2. Topic 3.2 · 19 minImplicit Differentiation
3. Topics 3.3–3.4 · 22 minDifferentiating Inverse Functions · Differentiating Inverse Trigonometric Functions
4. Topics 3.6, 3.5 · 23 minCalculating Higher-Order Derivatives · Selecting Procedures for Calculating Derivatives

Unit 4 Contextual Applications of Differentiation

1. Topics 4.1, 4.3 · 18 minInterpreting the Meaning of the Derivative in Context · Rates of Change in Applied Contexts Other Than Motion
2. Topic 4.2 · 20 minStraight-Line Motion: Connecting Position, Velocity, and Acceleration
3. Topics 4.4–4.5 · 21 minIntroduction to Related Rates · Solving Related Rates Problems
4. Topics 4.6–4.7 · 22 minApproximating Values of a Function Using Local Linearity and Linearization · Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms

Unit 5 Analytical Applications of Differentiation

1. Topic 5.1 · 18 minUsing the Mean Value Theorem
2. Topics 5.2, 5.5 · 19 minExtreme Value Theorem, Global Versus Local Extrema, and Critical Points · Using the Candidates Test to Determine Absolute (Global) Extrema
3. Topics 5.3–5.4 · 20 minDetermining Intervals on Which a Function Is Increasing or Decreasing · Using the First Derivative Test to Determine Relative (Local) Extrema
4. Topics 5.6–5.7 · 20 minDetermining Concavity of Functions over Their Domains · Using the Second Derivative Test to Determine Extrema
5. Topics 5.8–5.9 · 21 minSketching Graphs of Functions and Their Derivatives · Connecting a Function, Its First Derivative, and Its Second Derivative
6. Topics 5.10–5.11 · 21 minIntroduction to Optimization Problems · Solving Optimization Problems
7. Topic 5.12 · 21 minExploring Behaviors of Implicit Relations

Unit 6 Integration and Accumulation of Change

1. Topics 6.1–6.2 · 20 minExploring Accumulations of Change · Approximating Areas with Riemann Sums
2. Topics 6.3, 6.6 · 23 minRiemann Sums, Summation Notation, and Definite Integral Notation · Applying Properties of Definite Integrals
3. Topics 6.4–6.5 · 22 minThe Fundamental Theorem of Calculus and Accumulation Functions · Interpreting the Behavior of Accumulation Functions Involving Area
4. Topics 6.7–6.8 · 21 minThe Fundamental Theorem of Calculus and Definite Integrals · Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
5. Topic 6.9 · 24 minIntegrating Using Substitution
6. Topics 6.10, 6.14 · 20 minIntegrating Functions Using Long Division and Completing the Square · Selecting Techniques for Antidifferentiation
7. Topics 6.11–6.12 · BC only · 21 minIntegrating Using Integration by Parts · Integrating Using Linear Partial Fractions
8. Topic 6.13 · BC only · 19 minEvaluating Improper Integrals

Unit 7 Differential Equations

1. Topics 7.1–7.2 · 21 minModeling Situations with Differential Equations · Verifying Solutions for Differential Equations
2. Topics 7.3–7.4 · 20 minSketching Slope Fields · Reasoning Using Slope Fields
3. Topics 7.5, 7.9 · BC only · 22 minApproximating Solutions Using Euler’s Method · Logistic Models with Differential Equations
4. Topics 7.6–7.8 · 22 minFinding General Solutions Using Separation of Variables · Finding Particular Solutions Using Initial Conditions and Separation of Variables · Exponential Models with Differential Equations

Unit 8 Applications of Integration

1. Topics 8.2, 8.1 · 21 minConnecting Position, Velocity, and Acceleration of Functions Using Integrals · Finding the Average Value of a Function on an Interval
2. Topic 8.3 · 19 minUsing Accumulation Functions and Definite Integrals in Applied Contexts
3. Topics 8.4–8.6 · 19 minFinding the Area Between Curves Expressed as Functions of x · Finding the Area Between Curves Expressed as Functions of y · Finding the Area Between Curves That Intersect at More Than Two Points
4. Topics 8.7–8.8 · 22 minVolumes with Cross Sections: Squares and Rectangles · Volumes with Cross Sections: Triangles and Semicircles
5. Topics 8.9–8.10 · 22 minVolume with Disc Method: Revolving Around the x- or y-Axis · Volume with Disc Method: Revolving Around Other Axes
6. Topics 8.11–8.12 · 20 minVolume with Washer Method: Revolving Around the x- or y-Axis · Volume with Washer Method: Revolving Around Other Axes
7. Topics 8.13, 9.3 · BC only · 19 minThe Arc Length of a Smooth, Planar Curve and Distance Traveled · Finding Arc Lengths of Curves Given by Parametric Equations

Unit 9 Parametric Equations, Polar Coordinates, and Vector-Valued Functions

1. Topics 9.1–9.2 · BC only · 21 minDefining and Differentiating Parametric Equations · Second Derivatives of Parametric Equations
2. Topics 9.4–9.6 · BC only · 22 minDefining and Differentiating Vector-Valued Functions · Integrating Vector-Valued Functions · Solving Motion Problems Using Parametric and Vector-Valued Functions
3. Topic 9.7 · BC only · 20 minDefining Polar Coordinates and Differentiating in Polar Form
4. Topics 9.8–9.9 · BC only · 22 minFind the Area of a Polar Region or the Area Bounded by a Single Polar Curve · Finding the Area of the Region Bounded by Two Polar Curves

Unit 10 Infinite Sequences and Series

1. Topics 10.1–10.2 · BC only · 22 minDefining Convergent and Divergent Infinite Series · Working with Geometric Series
2. Topics 10.3–10.4 · BC only · 20 minThe nth Term Test for Divergence · Integral Test for Convergence
3. Topics 10.5–10.6 · BC only · 22 minHarmonic Series and p-Series · Comparison Tests for Convergence
4. Topics 10.7, 10.9, 10.8 · BC only · 23 minAlternating Series Test for Convergence · Determining Absolute or Conditional Convergence · Ratio Test for Convergence
5. Topics 10.12, 10.10 · BC only · 20 minLagrange Error Bound · Alternating Series Error Bound
6. Topic 10.11 · BC only · 19 minFinding Taylor Polynomial Approximations of Functions
7. Topic 10.13 · BC only · 20 minRadius and Interval of Convergence of Power Series
8. Topics 10.14–10.15 · BC only · 23 minFinding Taylor or Maclaurin Series for a Function · Representing Functions as Power Series