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       COURSE MATERIAL AND VIDEO LESSONS FOR AP CALCULUS (AB)     

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Unit 1: Functions 

What is a Function 

Finding Domain and Range

Composite Functions 

 Determining if a function is even, odd, or neither

Inverse of a Function

Absolute Value Function

Greatest Integer Function

Polynomial Functions and their Graphs

Finding zeros of a Quadratic Function

Rational Functions and their Graphs

Trigonometric Functions and their Graphs 

Inverse of Trigonometric Functions and their Graphs  

Domain and Range of Trigonometric Functions   

 Exponential Functions and their Graphs   

Logarithmic Functions and their Graphs    

Properties of Logarithm   

Average Rate of Change

Practice Problems

    Unit 2:      Limits and Continuity

 Evaluating one-sided limit by Direct Substitution

Evaluating one-sided limit by Factoring then Cancel

Evaluating one-sided limit by Rationalization
Trigonometric Limit - sin(u) over (u)
Evaluating Two-sided Limit

Determining limit from a Piecewise Function

Limit Involving Absolute Value

Graphing Piecewise Function

Limit To Infinity

Horizontal Asymptote, Vertical Asymptotes and Slant Asymptote

Continuity and Discontinuity of a Function

Types of Discontinuity

The Squeeze Theorem

The Extreme Value Theorem

The Intermediate Value Theorem 

Practice Problems

Unit 3: Differentiation

Differentiation from First Principle

The Power Rule

The Chain Rule

The Product Rule 

The Quotient Rule

Derivative of Trigonometric Functions

Derivative of Inverse Trigonometric Functions

Derivative of Logarithmic Functions 

Derivative of Exponential Functions  

Differentiability and Continuity of a Function

Estimating A derivative

Sketching First Derivative Functions

Interpreting First Derivative Graphs
Sketching Second Derivative Graphs

Implicit Differentiation

Derivative of the Inverse of a Function

The Mean Value Theorem

Rolle's Theorem

The Second derivative

 L'Hopital's Rule (Review of limits)

Practice Problems

Unit 4: Applications of Differential Calculus

Slope and Instantaneous Rate of Change

Equation of the Tangent Line

Equation of the The Normal Line 

Secant Line

Increasing and Decreasing Intervals

Finding Critical Values 

Relative/Local Maximum, Minimum and inflection Point

First Derivative Test

Second Derivative Test

 Concavity and Inflection Points

Global/Absolute Maximum or Minimum

End Behavior of a polynomial

Optimization: Problem Solving - Maxima snd Minima

Position, Velocity and Acceleration

Related Rates of Change

Practice Problems

Copyright © 2012 Peter Smith

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