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Course Design Overview

Working in Groups

Chapter 1: Review of Derivatives
Chapter 1 OVERVIEW
1.1:    The Power Rule and Exponential Rule
Explanation Example A      Example B     Example C
1.2:    Composite Functions and the Chain Rule
Explanation Example A      Example B     Example C      Example D
1.3:    Trig and Log Rules
Explanation     Example A    Example B     Example C     Example D
1.4:    Local Linearity and Approximations
Explanation     Example A      Example B
1.4:    Derivatives and Rectilinear Motion
Explanation     Example A     Example B     Example C
1.5:    The Product Rule
Explanation     Example A     Example B     Example C      Example D
1.5:    The Quotient Rule
Explanation     Example A     Example B     Example C      Example D
1.7:    Higher Order Derivatives
Explanation    Example A      Example B     Example C Example D
1.8:    Intro to AP: Basic Derivatives Numerically and Graphically
Explanation Part 1 Example A    Example B    Example C     Example D
Explanation Part 2 Example A    Example B

Chapter 2: Anti-Derivatives
Chapter 2 OVERVIEW
2.1:    The Anti-Power and Transcendental Rules
Explanation     Example A       Example B     Example C      Example D
Common Errors in Integration
Explanation
2.2:    Anti-Derivatives and Initial Conditions
Explanation     Example A     Example B     Example C
2.3:    Anti-Derivatives and Motion
Explanation     Example A     Example B     Example C
2.4:    Integration by Substitution--the Chain Rule
Explanation     Example A      Example B     Example C      Example D
Alternative Explanation (Murphy)
2.4:    The Transcendental Rules and Integration by Substitution
Explanation     Example A      Example B     Example C      Example D
2.5:    Derivatives and AntiDerivatives in Context: Motion
Explanation Example A      Example B     Example C      Example D/E
2.6:    Separable Differential Equations
Explanation     Example A      Example B     Example C      Example D Example E                          2.7:    Creating Slope Fields
Explanation    Example A      Example B     Example C     Example D
2.7:    Reading Slope Fields
Explanation    Examples A-C     Examples D-F

Chapter 3: Definite Integrals
Chapter 3 OVERVIEW
3.1:    The Fundamental Theorem of Calculus
Explanation    Example A      Example B     Example C      Example D
3.2:    Definite Integrals and Integration by Substitution
Explanation    Example A      Example B     Example C      Example D
3.3:    Context: Area, Displacement, and Net Change
Explanation     Example A      Example B     Example C      Example D
3.4:    Intro to AP:   Accumulation of Rates
Explanation   Example A      Example B     Example C      Example D
3.5:    Definite Integrals, Riemann Rectangles, and Trapezoidal Rule
– Riemann Sums
Explanation   Example A      Example B     Example C      Example D     Example E
– Trapezoidal Rule
Explanation   Example A      Example B     Example C      Example D
3.6:   Intro to AP:   Table Problems
Explanation   Example A     Example B      Example C

Chapter 4 Applications of Derivatives
Chapter 4 OVERVIEW
4.1:    Extrema and the Derivative Tests
     Extrema:    Explanation
     The First and Second Derivative Tests :
        Explanation     Example A      Example B     Example C      Example D      Example E
4.2:    Optimization
Explanation     Example A      Example B     Example C
4.3:   The Mean Value and Extreme Value Theorems
Explanation     Example A      Example B     Example C
4.4:     Intro to AP: Input-Output Problems
Explanation     Example A     Example B     Example C
4.5:     The Second Derivative, Points of Inflection, and Concavity
Explanation     Example A     Example B     Example C     Example D
4.6:    Graphing with Derivatives
Explanation     Example A      Example B     Example C      Example D       Example E
4.7:    Graphical Analysis I
Explanation    Example A      Example B      Example C     Example D        Example E
4.8: Graphical Analysis II
Explanation     Example A      Example B     Example C      Example D

Chapter 5 Derivatives as Rate of Change
Chapter 5 OVERVIEW
5.1:    Motion
Explanation     Example A      Example B     Example C      Example D/E
5.2:    Models of Growth and Decay
Explanation     Example A      Example B     Example C/D
5.2:    Simple Bounded Growth
Explanation     Example A      Example B     Example C
5.2:    Logistic Growth
Explanation Example A      Example B     Example C      Example D
5.3:    Implicit Differentiation
Explanation   Example A      Example B     Example C      Example D
5.4:    Implicit Differentiation FRQs
Explanation   Example A      Example B
5.5:    Related Rates
Explanation     Example A      Example B     Example C Recap

Chapter 6: Applications of Integrals
Chapter 6 OVERVIEW
6.1:   Area between Two Curves
Explanation
Example A      Example B     Example C     Example D
6.2:   Arc Length
Explanation Example A      Example B     Example C      Example D

Intro To Volume

6.3 Part 1:   Volume by Rotation about an Axis: Disk Method
Explanation    Example A      Example B
6.3 Part 2:   Volume by Rotation about an Axis: Washer Method
Explanation     Example A      Example B/C
6.5:   Volume by Rotation about a Line not an Axis
Explanation     Example A      Example B     Example C
6.6:   Volume by Cross-section Method
Explanation     Example A and B     Example C      Example D     Example E
6.7:   AP Volume FRQs
Explanation    Example A     Example B      Example C
6.7:   Volume by Shell Method
Explanation    Example A Example B

Chapter 7: Limits, Continuity and Differentiability
Chapter 7 OVERVIEW
7.1:    Limits and L’Hopital’s Rule
Basic Limits
Explanation     Example A     Example B     Example C     Example D
L’Hopital’s Rule
Explanation     Example A     Example B     Example C     Example D
7.2:     The Limit Definitions of a Derivative
Explanation     Example A     Example B     Example C     Example D
7.3:    One-sided and Infinite Limits
Explanation     Example A     Example B     Example C     Example D
7.4:    Continuity
Explanation     Example A     Example B     Example C     Example D
7.5:    Differentiability and Smoothness
Explanation     Example A     Example B     Example C     Example D
7.6:    Limits at Infinity and End Behavior
Explanation     Example A     Example B     Example C     Example D

Chapter 8:    AP Free Response Review
Chapter 8 OVERVIEW
8.1:    Accumulation of Rates
Explanation     Tombstone Mine Problem
8.2:    Reasoning from Tabular Data
Explanation     Dr. Q's Solar Panels
8.3:    Graphical Analysis
Explanation     Graphical Analysis Problem
8.4:    Rectilinear Motion
Explanation     The Two Particle Problem
8.5:    Differential Equations
Explanation     The Parachute Problem
8.6:    Area & Volume
Explanation     The Wooden Table Problem
8.7:    Related Rates
Explanation     The Two Train Problem
8.8:   Implicit Differentiation
Explanation.     The Implicit Diff problem
8.9:    Miscellaneous Topics
Explanation      Miscellaneous Topics Problem