Version #1
​The course below follows CollegeBoard's Course and Exam Description.  It was built for a 45-minute class period that meets every day, so the lessons are shorter than our Calculus Version #2. 

Unit 0 - Calc Prerequisites (Summer Work)
        0.1 Summer Packet

Unit 1 - Limits and Continuity
        1.1 Can Change Occur at an Instant?
        1.2 Defining Limits and Using Limit Notation
        1.3 Estimating Limit Values from Graphs
        1.4 Estimating Limit Values from Tables
        1.5 Determining Limits Using Algebraic Properties
              (1.5 includes piecewise functions involving limits)
        1.6 Determining Limits Using Algebraic Manipulation
        1.7 Selecting Procedures for Determining Limits
              (1.7 includes rationalization, complex fractions, and                    absolute value)
        1.8 Determining Limits Using the Squeeze Theorem
        1.9 Connecting Multiple Representations of Limits
        Mid-Unit Review - Unit 1
        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 Infinite Limits and Vertical Asymptotes
        1.15 Limits at Infinity and Horizontal Asymptotes
        1.16 Intermediate Value Theorem (IVT)
        Review - Unit 1

Unit 2 - Differentiation: Definition and Fundamental Properties
        2.1 Defining Average and Instantaneous Rate of
              Change at a Point
        2.2 Defining the Derivative of a Function and Using
              Derivative Notation
              (2.2 includes equation of the tangent line)
        2.3 Estimating Derivatives of a Function at a Point
        2.4 Connecting Differentiability and Continuity
        2.5 Applying the Power Rule
        2.6 Derivative Rules: Constant, Sum, Difference, and
              Constant Multiple
              (2.6 includes horizontal tangent lines, equation of the
                normal line, and differentiability of piecewise)
        2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)
        2.8 The Product Rule
        2.9 The Quotient Rule
        2.10 Derivatives of tan(x), cot(x), sec(x), and csc(x) 
        Review - Unit 2

Unit 3 - Differentiation: Composite, Implicit, and Inverse Functions
        3.1 The Chain Rule
        3.2 Implicit Differentiation
        3.3 Differentiating Inverse Functions
        3.4 Differentiating Inverse Trigonometric Functions
        3.5 Selecting Procedures for Calculating Derivatives
        3.6 Calculating Higher-Order Derivatives
        Review - Unit 3

Unit 4 - Contextual Applications of Differentiation
        4.1 Interpreting the Meaning of the Derivative in Context
        4.2 Straight-Line Motion: Connecting Position, Velocity,
              and Acceleration
        4.3 Rates of Change in Applied Contexts Other Than
              Motion
        4.4 Introduction to Related Rates
        4.5 Solving Related Rates Problems
        4.6 Approximating Values of a Function Using Local
              Linearity and Linearization
        4.7 Using L'Hopital's Rule for Determining Limits of
              Indeterminate Forms
       Review - Unit 4

Unit 5 - Analytical Applications of Differentiation
        5.1 Using the Mean Value Theorem
        5.2 Extreme Value Theorem, Global Versus Local
              Extrema, and Critical Points
        5.3 Determining Intervals on Which a Function is
              Increasing or Decreasing
        5.4 Using the First Derivative Test to Determine Relative
              Local Extrema
        5.5 Using the Candidates Test to Determine Absolute
              (Global) Extrema
        5.6 Determining Concavity of Functions over Their
              Domains
         5.7 Using the Second Derivative Test to Determine
               Extrema
        Mid-Unit Review - Unit 5
        5.8 Sketching Graphs of Functions and Their Derivatives
        5.9 Connecting a Function, Its First Derivative, and Its
              Second Derivative
              (5.9 includes a revisit of particle motion and
               determining if a particle is speeding up/down.)
        5.10 Introduction to Optimization Problems
        5.11 Solving Optimization Problems
        5.12 Exploring Behaviors of Implicit Relations
        Review - Unit 5

Unit 6 - Integration and Accumulation of Change
        6.1 Exploring Accumulation of Change
        6.2 Approximating Areas with Riemann Sums
        6.3 Riemann Sums, Summation Notation, and Definite
              Integral Notation
        6.4 The Fundamental Theorem of Calculus and
              Accumulation Functions
        6.5 Interpreting the Behavior of Accumulation Functions
​              Involving Area
        Mid-Unit Review - Unit 6
        6.6 Applying Properties of Definite Integrals
        6.7 The Fundamental Theorem of Calculus and Definite
              Integrals
        6.8 Finding Antiderivatives and Indefinite Integrals:
              Basic Rules and Notation
        6.9 Integrating Using Substitution
        6.10 Integrating Functions Using Long Division
​                and Completing the Square
        6.11 Integrating Using Integration by Parts (BC topic)
        6.12 Integrating Using Linear Partial Fractions (BC topic)
        6.13  Evaluating Improper Integrals (BC topic)
        6.14 Selecting Techniques for Antidifferentiation
        Review - Unit 6

Unit 7 - Differential Equations
        7.1 Modeling Situations with Differential Equations
        7.2 Verifying Solutions for Differential Equations
        7.3 Sketching Slope Fields
        7.4 Reasoning Using Slope Fields
        7.5 Euler's Method (BC topic)
        7.6 General Solutions Using Separation of Variables
        7.7 Particular Solutions using Initial Conditions and
             Separation of Variables
        7.8 Exponential Models with Differential Equations
        7.9 Logistic Models with Differential Equations (BC topic)
        Review - Unit 7

Unit 8 - Applications of Integration
        8.1 Average Value of a Function on an Interval
        8.2 Position, Velocity, and Acceleration Using Integrals
        8.3 Using Accumulation Functions and Definite Integrals
              in Applied Contexts
        8.4 Area Between Curves (with respect to x)
        8.5 Area Between Curves (with respect to y)
        8.6 Area Between Curves - More than Two Intersections
        Mid-Unit Review - Unit 8
        8.7 Cross Sections: Squares and Rectangles
        8.8 Cross Sections: Triangles and Semicircles
        8.9 Disc Method: Revolving Around the x- or y- Axis
        8.10 Disc Method: Revolving Around Other Axes
        8.11 Washer Method: Revolving Around the x- or y-Axis
        8.12 Washer Method: Revolving Around Other Axes
        8.13 The Arc Length of a Smooth, Planar Curve and
                Distance Traveled (BC topic)
        Review - Unit 8

Unit 9 - Parametric Equations, Polar Coordinates, and Vector-Valued Functions  (BC topics)
        9.1 Defining and Differentiating Parametric Equations
        9.2 Second Derivatives of Parametric Equations
        9.3 Arc Lengths of Curves (Parametric Equations)
        9.4 Defining and Differentiating Vector-Valued Functions
        9.5 Integrating Vector-Valued Functions
        9.6 Solving Motion Problems Using Parametric and
              Vector-Valued Functions            
        9.7 Defining Polar Coordinates and Differentiating in
              Polar Form
        9.8 Find the Area of a Polar Region or the Area Bounded
              by a Single Polar Curve
        9.9 Finding the Area of the Region Bounded by Two
              Polar Curves
        Review - Unit 9

Unit 10 - Infinite Sequences and Series (BC topics)
        10.1 Defining Convergent and Divergent Infinite Series
        10.2 Working with Geometric Series
        10.3 The nth Term Test for Divergence
        10.4 Integral Test for Convergence
        10.5 Harmonic Series and p-Series
        10.6 Comparison Tests for Convergence
        10.7 Alternating Series Test for Convergence
        10.8 Ratio Test for Convergence
​        10.9 Determining Absolute or Conditional Convergence
        Mid-Unit Review - Unit 10
​        10.10 Alternating Series Error Bound
        10.11 Finding Taylor Polynomial Approximations of
                  Functions
        10.12 Lagrange Error Bound
        10.13 Radius and Interval of Convergence of Power
                  Series
        10.14 Finding Taylor Maclaurin Series for a Function
        10.15 Representing Functions as a Power Series
        Review - Unit 10

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