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AP Calculus AB and BC:  Video Lessons are linked below.


Unit 1:  Limits and Continuity (Unit 1 Playlist)

1.01 -- Introducing Calculus:  Can Change Occur at an Instant?
1.02 -- Defining Limits and Using Limit Notation
1.03 -- Estimating Limit Values from Graphs
1.04 -- Estimating Limit Values from Tables
1.05 -- Determining Limits Using Algebraic Properties of Limits  (this topic has THREE videos:  VIDEO 1,  VIDEO 2, and VIDEO 3.)
1.06 -- Determining Limits Using Algebraic Manipulations (this topic has TWO videos:  VIDEO 1 and VIDEO 2)
1.07 -- Selecting Procedures for Determining Limits
1.08 -- Determining Limits Using Squeeze Theorem
1.09 -- Connecting Multiple Representations of Limits
1.10 -- Exploring Types of Discontinuities
1.11 -- Defining Continuity at a Point
1.12 -- Confirming Continuity over an Interval
1.13 -- Removing Discontinuities
1.14 -- Connecting Infinite Limits and Vertical Asymptotes
1.15 -- Connecting Limits at Infinity and Horizontal Asymptotes
1.16 -- Working with the Intermediate Value Theorem (IVT)

Unit 2:  Differentiation (Definition and Fundamental Properties)  (Unit 2 Playlist)

2.01 -- Defining Average and Instantaneous Rates of Change at a Point
2.02 -- Defining the Derivative of a Function and Using Derivative Notation
2.03 -- Estimating Derivatives of a Function at a Point
2.04 -- Connecting Differentiability and Continuity:  Determining When Derivatives Do and Do Not Exist
2.05 -- Applying the Power Rules
2.06 -- Derivative Rules:  Constant, Sum, Difference, and Constant Multiple
2.07 -- Derivatives of cos(x), sin(x), e^x, and ln(x)
2.08 -- The Product Rule
2.09 -- The Quotient Rule
2.10 -- Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

Unit 3:  Differentiation (Composite, Implicit, and Inverse Functions)   (Unit 3 Playlist)

3.01 -- The Chain Rule
3.02 -- Implicit Differentiation
3.03 -- Differentiating Inverse Functions (this topic has TWO videos:  VIDEO 1 and VIDEO 2)
3.04 -- Differentiating Inverse Trigonometric Functions
3.05 -- Selecting Procedures for Calculating Derivatives
3.06 -- Calculating Higher-Order Derivatives

Unit 4:  Contextual Applications of Differentiation  (Unit 4 Playlist)

4.01 -- Interpreting the Meaning of the Derivative in Context
4.02 -- Straight-Line Motion:  Connecting Position, Velocity, and Acceleration
4.03 -- Rates of Change in Applied Contexts Other Than Motion
4.04 -- Introduction to Related Rates
4.05 -- Solving Related Rates Problems
4.06 -- Approximating Values of a Function Using Local Linearity and Linearization
4.07 -- Using L'Hopital's Rule for Determining Limits of Indeterminate Forms

Unit 5:  Analytical Applications of Differentiation  (Unit 5 Playlist)

5.01 -- Using the Mean Value Theorem (MVT)
5.02 -- Extreme Value Theorem (EVT), Global Versus Local Extrema, and Critical Points
5.03 -- Determining Intervals on Which a Function is Increasing or Decreasing
5.04 -- Using the First Derivative Test to Determine Relative (Local) Extrema
5.05 -- Using the Candidates Test to Determine Absolute (Global) Extrema
5.06 -- Determine Concavity of Functions over Their Domains
5.07 -- Using the Second Derivative Test to Determine Extrema
5.08 -- Sketching Graphs of Functions and Their Derivatives
5.09 -- Connecting a Function to its First Derivative and its Second Derivative
5.10 -- Introduction to Optimization
5.11 -- Solving Optimization Problems
5.12 -- Exploring Behaviors of Implicit Relations

​Unit 6:  Integration and Accumulation of Change  (Unit 6 Playlist)

6.01 -- Exploring Accumulations of Change
6.02 -- Approximating Areas with Riemann Sums
6.03 -- Riemann Sums, Summation Notation, and Definite Integral Notation
6.04 -- The Fundamental Theorem of Calculus and Accumulation Functions
6.05 -- Interpreting the Behavior of Accumulation Functions Involving Area
6.06 --Applying Properties of Definite Integrals
6.07 -- The Fundamental Theorem of Calculus and Definite Integrals
6.08 -- Finding the Antiderivatives and Indefinite Integrals:  Basic Rules and Notation
6.09 -- Integration Using Substitution (U-Sub)
6.10 -- Integrating Functions Using Long Division and Completing the Square
BC ONLY 6.11 -- Integrating Using Integration by Parts
BC ONLY 6.12 -- Using Linear Partial Fractions
BC ONLY 6.13 -- Evaluating Improper Integrals
6.14 -- Selecting Techniques for Antidifferentiation

Unit 7:  Differential Equations  (Unit 7 Playlist)

7.01 -- Modeling Situations with Differential Equations
7.02 -- Verifying Solutions for Differential Equations
7.03 -- Sketching Slope Fields
7.04 -- Reasoning Using Slope Fields
BC ONLY 7.05 -- Approximating Solutions Using Euler's Method
7.06 -- Finding General Solutions Using Separation of Variables
7.07 -- Finding Particular Solutions Using Initial Conditions and Separation of Variables
7.08 -- Exponential Models with Differential Equations
BC ONLY 7.09 -- Logistic Models with Differential Equations

Unit 8: Applications of Integration  (Unit 8 Playlist)

8.01 -- Finding the Average Value of a Function on an Interval
8.02 -- Connecting Position, Velocity, and Acceleration of Functions Using Integrals
8.03 -- Using Accumulation Functions and Definite Integrals in Applied Contexts
8.04 -- Finding the Area Between Curves Expressed as Functions of x
8.05 -- Finding the Area Between Curves Expressed as Functions of y
8.06 -- Finding the Area Between Curves That Intersect at More Than Two Points
8.07 -- Volumes with Cross Sections:  Squares and Rectangles
8.08 -- Volumes with Cross Sections:  Triangles and Semicircles
8.09 -- Volume with Disc Method:  Revolving Around the x- or y-axis
8.10 -- Volume with Disc Method:  Revolving Around Other Axes
8.11 -- Volume with Washer Method:  Revolving Around the x- or y-axis
8.12 -- Volume with Washer Method:  Revolving Around Other Axes
BC ONLY 8.12 The Arc Length of a Smooth, Planar Curve and Distance Traveled

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

BC ONLY 9.01 -- Defining and Differentiating Parametric Equations
BC ONLY 9.02 -- Second Derivatives of Parametric Equations
BC ONLY 9.03 -- Finding Arc Lengths of Curves Given by Parametric Equations
BC ONLY 9.04 -- Defining and Differentiating Vector-Valued Functions
BC ONLY 9.05 -- Integrating Vector-Valued Functions
BC ONLY 9.06 -- Solving Motion Problems Using Parametric and Vector-Valued Functions
BC ONLY 9.07 -- Defining Polar Coordinates and Differentiating in Polar Form
BC ONLY 9.08 -- Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
BC ONLY 9.09 -- Finding the Area of the Region Bounded by Two Polar Curves

BC ONLY Unit 10:  Infinite Sequences and Series (Unit 10 Playlist)

BC ONLY 10.01 -- Defining Convergent and Divergent Infinite Series
BC ONLY 10.02 -- Working with Geometric Series
BC ONLY 10.03 -- The nth Term Test for Divergence
BC ONLY 10.04 -- Integral Test for Convergence
BC ONLY 10.05 -- Harmonic Series and p-series
BC ONLY 10.06 -- Comparison Tests for Convergence
BC ONLY 10.07 -- Alternating Series Test for Convergence
BC ONLY 10.08 -- Ratio Test for Convergence
BC ONLY 10.09 -- Determining Absolute or Conditional Convergence
BC ONLY 10.10 -- Alternating Series Error Bound
BC ONLY 10.11 -- Finding Taylor Polynomial Approximations of Functions
BC ONLY 10.12 -- Lagrange Error Bound
BC ONLY 10.13 -- Radius and Interval of Convergence of Power Series
BC ONLY 10.14 -- Finding Taylor or Maclaurin Series for a Function
BC ONLY 10.15 -- Representing Functions as Power Series