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 Velocity     Definition of the Derivative and its         Graph     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 Miscellaneous 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         Mean Value 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

Send any comments or questions to: David Pleacher