A.P. Calculus Course -- Day by Day
Using Anton's 8th Edition (Single Variable)

I. Precalculus Review
        Introduction to Calculus
        Trigonometry Review
        Absolute Value and Symmetry
        Slope and Equations of Lines
        Functions -- Domain and Range
        Types of Functions; Inverse Functions
        Infinite Geometric Series
        Mini Exam #1 -- Precalculus

II. Limits and Continuity
        Fractals
        Fractal Applications
        Intuitive Approach to Limits
        Computation of Limits
        Delta-Epsilon Definition of Limits
        Hexaflexagons
        Continuity
        Limits of Trigonometric Functions
        Limits with a Calculator
        Review of Limits and Continuity
        Test on Functions, Limits, and Continuity (chapter 2)

III. Derivatives
        Rates of Change and Vedlocity
        Definition of the Derivative and its Gaph
        Power Rule
        Product Rule
        Quotient Rule
        Proofs of Derivatives of Trig Functions
        Review for Test on Basic Derivative Formulas
        Test on Basic Derivative Formulas (sections 3.1 - 3.5)
        Chain Rule (2 Forms)
        Chain Rule Review
        Proof of Quotient Rule / Parametric Equations
        The Football Kick (Parametric Equations)
        Differentials
        Differentials /Linear Approximation
        Derivative Review
        Review for Test
        Test on Derivatives (Chapter 3)

IV. Logarithmic and Exponential Functions
        Implicit Differentiation
        Implicit Differentiation
        Logarithms
        Exponential Functions, e, and pi
        Exponential Functions -- M&M activity
        Compound Interest and Quiz on Logs
        Graphs of Exponential and Logarithmic Functions
        Video on Exponential Functions
        Derivatives of Logarithmic functions
        Derivatives of Exponential Functions
        Logarithmic Differentiation
        Introduction to Related Rates Problems
        Related Rates Problems
        Related Rates Problems
        Review for Mini Exam #2
        Mini Examination #2 (Chapters 2 and 3)
        Review for Test on Exponential and Logarithmic functions
        Test on Exponential and Logarithmic functions

V. Inverse Trigonometric Functions and Misc. Topics
        Review of Inverse Trigonometric Functions
        Derivatives of Inverse Trig Functions
        L'Hopital's Rule
        L'Hopital's Rule
        Review of Derivatives
        Test on Derivatives (Chapter 4)

VI. Analysis of Functions and their Graphs
        Increasing / Decreasing Functions
        Concavity
        Relative Maxima / Minima and Points of Inflection
        Review of maxima/minima
        Review for Semester Examination
        First Semester Examination Part I (With a Calculator)
        Review for First Semester Exam
        First Semester Examination Part II (Without a Calculator)

VII. Applications of the Derivative
        Absolute Maxima and Minima
        Introduction to Applied Maximum and Minimum Problems (Box Problem)
        Applied Maximum and Minimum Problems (Fence Problem)
        Applied Maximum and Minimum Problems (Tin Can Problem)
        Applied Maximum and Minimum Problems (Mini Golf Problem)
        Minimum Distance Problem
        Rectilinear Motion
        Newton's Method
        Rolle's Theorem and the MeanValue Theorem
        Maximum and Minimum Problems -- Spider and the Fly
        Review for Test on chapter 5
        Test on chapter 5

VIII. Integration
        Introduction to the Indefinite Integral
        Integration Formulas
        The Exact Differential
        More on the Exact Differential
        Velocity and Acceleration Revisited
        Review for Test on Basic Integration Formulas
        Test on basic Integration formulas
        Proof By Induction
        Area Under A Curve -- with Rectangles
        Exact Area Under a Curve using Limits
        Introduction to Differential Equations
        Video on Integration and Quiz on Induction
        Slope Fields
        The Definite Integral and Area Under a Curve
        Fundamental Theorem and Properties of the Definite Integral
        The Fundamental Theorem and Area Under a Curve
        Total Distance versus Displacement
        Review for Test on Sections 6.1 - 6.6
        Test on Sections 6.1 - 6.6
        Average Value of a Function
        Substitution in the Definite Integral
        The Logarithm as an Integral
        Mini Examination #3 (chapters 4, 5, 6, 7)
       

IX. Applications of the Definite Integral
        Area Between Two Curves
        Area Between Two Curves
        Volumes of Solids of Revolution (Disk Method)
        Volumes of Solids of Revolution (Washer Method)
        Volumes of Solids of Revolution (Shell Method)
        Volumes of Solids of Revolution (Washer and Shell Methods)
        Arc Length
        Review for Test on Chapter 7
        Test on Chapter 7

X. Techniques of Integration
        Review of Basic Integration Formulas
        Integration by Parts
        Integration by Parts -- Reduction Formula
        Integration by Parts -- Escalante's Method
        Integrals Involving odd powers of sine and cosine
        Integrals Involving even powers of sine and cosine
        Integrals Involving odd powers of secant and tangent
        Integrals Involving even powers of secant and tangent
        Test on Sections 9.1 - 9.3
        Integrals Involving Trigonometric Substitution
        Integrals Involving Trigonometric Substitution (Day 2)
        Integrals Involving Quadratics
        Integrals Involving Partial Fractions
        Partial Fractions (Heaviside Method)
        Review of Integration Techniques
        Review of Integration -- Silly Sally Seal
        Numerical Methods of Integration
        "Really Stupid Integrals"
        Test on Chapter 9

XI. Review for A.P. Exam
        1991 A.P. Exam Grading Standards
        Calculator Review for the A.P.
        A.P. Exam Review
        Final Exam M/C Part A
        Final Exam M/C part B
        Tips for A.P. Exam
        Review for A.P Exam
        Final Exam F/R Part A
        Final Exam F/R Part B
        Review for A.P Exam
        Review for A.P Exam

XII. Analytic Geometry
        Circles
        Parabolas
        Parabolas
        Circles, Parabolas, and Lines (Game)
        Ellipses
        Ellipses
        Hyperbolas
        Circle and Parabola Activities
        Graphing Conics
        Applications of Conics
        Rotation of Axes
        Tracker Game -- with conics
        Test on Analytic Geometry

XIII. Polar Coordinates
        Introduction to Polar Coordinates
        Graphing Polar Coordinates
        Conversion Between Polar and Cartesian Coordinates
        Polar Coordinates Battleship Game
        Review for Polar Coordinates Test
        Polar Coordinates Test
        The Last Day of Calculus