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 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
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