Unit 1Limits and Continuity 
4 lessons4 Weeks
Limits and Continuity 
 Week 1
Lesson 1
Instantaneous Change and Limits
We'll begin by motivating the study of differential calculus in the context of instantaneous change.  We will then introduce limits as a method of finding instantaneous rates.  Finally, we will learn to analyze right, left, and overall limits graphically.
 Week 2
Lesson 2
Limit Properties
In this class, we'll look at the linearity of the limit, and limits of products and quotients.  This class will meld into lesson 3, so we'll begin introducing some algebraic techniques for evaluating limits. 
 Week 3
Lesson 3
Algebraic Limits
Picking up from week 2, we'll look at finding limits via factorization, conjugate multiplication, and squeeze theorem. 
 Week 4
Lesson 4
Continuity and the IVT
We will look at the three conditions for continuity at a point, working through both graphical and algebraic applications.  We will then introduce the intermediate value theorem.  
Unit 2Differentiation
4 lessons4 Weeks
Differentiation
 Week 5
Lesson 5
Introduction to the Derivative
Having covered limits, we'll begin by looking at the limit definition of the derivative.  We will then cover the basic derivatives students should memorize - basic trig, exponential, polynomial, logarithmic. 
 Week 6
Lesson 6
Product and Quotient Rule
We'll introduce product rule and quotient rule.  
 Week 7
Lesson 7
Chain Rule
We'll begin with a brief review of composite functions, and then introduce the chain rule for derivatives. 
 Week 8
Lesson 8
Implicit Differentiation 
We'll start off by motivating the need for implicit differentiation by looking at inverse functions and implicit functions.  We will then work through the process of implicit differentiation.
Unit 3Applications of the Derivative
8 lessons8 Weeks
Applications of the Derivative
 Week 9
Lesson 9
Position, Velocity, Acceleration
We'll look at velocity and acceleration as derivatives, and begin diving into more FRQ applications.
 Week 10
Lesson 10
Tangent Line approximation
We'll begin with finding tangent lines to functions, then move on to seeing how to use tangent lines for estimation.  We will also discuss how concavity informs whether an estimate is an overestimate vs. underestimate.  Finally, we will look at more complex applications, including tangent line approximation for implicit functions.
 Week 11
Lesson 11
Related Rates
 Week 12
Lesson 12
L'hopital's Rule
 Week 13
Lesson 13
The MVT and EXT
 Week 14
Lesson 14
Local Maxima and Minima
 Week 15
Lesson 15
Global Maxima and Minima
 Week 16
Lesson 16
Optimization
Unit 4Integration
5 lessons5 Weeks
Integration
 Week 17
Lesson 17
Riemann Sums 1
 Week 18
Lesson 18
Riemann Sums 2
 Week 19
Lesson 19
The Fundamental Theorem of Calculus
 Week 20
Lesson 20
Integration by Substitution 
 Week 21
Lesson 21
Further Integration Techniques
Unit 5Applications of the Integral
6 lessons6 Weeks
Applications of the Integral
 Week 22
Lesson 22
Accumulation of Change
 Week 23
Lesson 23
Area between Curves
We'll look at finding areas between curves, including orientation along the y-axis vs. x-axis.  We'll also look at cases where the intersection results in multiple regions.
 Week 24
Lesson 24
Volume: Cross Sections
We'll establish a general approach to finding volumes given cross sections, looking at triangular, semi-circular, and rectangular cross sections, among others.
 Week 25
Lesson 25
Volume: Disk Method
Using reasoning from the previous week, we will derive the formula for finding the volume of a solid of revolution.  We'll look at volumes of revolution about the x-axis and the y-axis.
 Week 26
Lesson 26
Volume: Washer Method
 Week 27
Lesson 27
Position, Velocity, and Acceleration
Unit 6Differential Equations
5 lessons5 Weeks
Differential Equations
 Week 28
Lesson 28
Modeling with Differential Equations
 Week 29
Lesson 29
Slope Fields
 Week 30
Lesson 30
Separation of Variables
 Week 31
Lesson 31
AP Review
 Week 32
Lesson 32
AP Review