The PreCalculus Project Screen Casts
by Kevin Quattrin, Brian Murphy, & Paul Maychowitz

How to Watch a Screencast

Course Design Overview

Working in Groups

Introduction:   General Preview of Analytic Geometry and Calculus

Chapter 1:         Analytic Trigonometry
Chapter 1 Overview
1-1         Analytic Trigonometry  
Explanation      Example A     Example B     Example C & D     Example E    
1-2         The Unit Circle and Special Triangles
Radian Explanation           
Unit Circle Explanation     Example A     Example B, c, & D     Example E
1-3         Calculator Use         
Explanation     Example A     Example B     Example C     Example D
1-4         Vectors Basics
Explanation     Example A     Example B     Example C     Example D
1-4         Vectors Conversions and Sums
Explanation     Example A     Example B     Example C     Example D
 

Chapter 2:         Parent Trigonometric Functions
Chapter 2 Overview: Types and Traits of Parent Trigonometric Functions  
2-1:         Sketching Trigonometric Functions
Explanation     Example A     Example B     Example C     Example D 
     Point-by-Point plotting of Sinusoidals 
2-1:         Finding the Equations of a Sinusoidal
Explanation     Example A     Example B     Example C     Example D 
2-2:         Solving Sinusoidal Equations   
Explanation     Example A     Example B     Example C     Example D
2-3:         Mathematical Modeling with Sinusoidals 
Explanation    Example A     Example B     Example C      
2-4:         Reciprocal and Quotient Curves  
Explanation     Example A     Example B     Example C     Example D 


Chapter 3:         Trigonometric Identities
Chapter 3 Overview
3-1         Quotient, Reciprocal, and Pythagorean Identities
Explanation      Example A     Example B     Example C     Example D
3-2         Basic Trig Identities and Factoring I
Explanation      Example A     Example B     Example C     Example D
3-2         Basic Trig Identities and Factoring II
Factoring Review
Explanation      Example A     Example B     Example C     Example D
3-3         Composite Argument and Even/Odd Rules
Explanation      Example A     Example B     Example C     Example D
Proof of the Composite Rules
3-4         Double Angle Rules  
Explanation      Example A     Example B     Example C     Example D  
3-5         Half Angle Rules  
Explanation      Example A     Example B     Example C 
3-6         Solving Equations with Identities and Algebra  
Explanation      Example A     Example B     Example C     Example D
3-7         Sum and Product Rules  
Explanation      Example A     Example B     Example C    Example D
3-8         Linear Combination of Sinusoidals 
Explanation      Example A     Example B     Example C     Example D

Chapter 4:         PreCalculus Basics
Chapter 4 Overview                                                                               
4-1:         Review of Linear Functions  
Explanation     Example A     Example B     Example C      
4-2:         Review of Quadratic Functions 
Explanation     Example A     Example B     Example C     Example D  
4-3:         Finding Complete Graphs of Polynomials   
Explanation Part I       Explanation Part II        Explanation Part III 
Example A     Example B     Example C     Example D
4-4:         Optimization by Calculator  
Explanation     Example A     Example B     Example C     Example D   
Additional:    Explanation Part 1   Explanation Part 2  
4-5:         Zeros of Higher Order Polynomials by Synthetic Substitution   
Explanation     Example A     Example B     Example C     Example D
4-6:         Sign Patterns 
Explanation Part 1             Explanation Part 2
Example A     Example B     Example C     Example D


Chapter 5:         Limits and Derivatives 
Chapter 5 Overview
5-1:         The Indeterminate Forms and Limits      
Explanation     Example A     Example B     Example C     Example D
5-2:         The Limit Definition of the Derivative       
Explanation     Example A     Example B     Example C     Example D
5-3:         The Power Rule       
Explanation     Example A     Example B     Example C     Example D
Proof of the Power Rule
5-4:         Local Linearity and Approximations     
Explanation     Example A     Example B     Example C     Example D
5-5:         Rectilinear Motion    
Explanation     Example A     Example B     Example C     Example D   
5-6:         Parametric Motion       
Explanation     Example A     Example B     Example C     Example D
Graphing Parametric Motion


Chapter 6:         Polynomial Functions                                                                
Chapter 6 Overview                                                                     
6-1:         Critical Values and Extremes of a Polynomial Function       
Explanation     Example A     Example B     Example C     Example D       
6-2:         Interpreting the Sign Pattern of the First Derivative  (The First Derivative Test) 
Explanation     Example A     Example B     Example C     Example D            
6-3:         Optimization Problems     
Explanation     Example A     Example B     Example C
6-4:         General Polynomial Sketching   
Explanation     Example A     Example B     Example C     Example D     Example E
 

Chapter 7:         Rational Functions                                                               
Chapter 7 Overview: Types and Traits of Rational Functions 
7-1:         Zeros, Vertical Asymptotes, and POEs 
Explanation     Example A     Example B     Example C     Example D
7-2:         Sign Patterns and Rational Functions  
Explanation     Example A     Example B     Example C     Example D
7-3 & 7-4:         End Behavior: Horizontal and Slant Asymptotes 
Explanation     Example A     Example B     Example C     Example D     Example E
7-5:         Derivatives: The Quotient Rule  
Explanation     Example A     Example B     Example C     Example D
7-6:         General Rational Curve Sketching
Explanation     Example A     Example B     Example C     Example D     Example E
7-7:         Rational Functions and the Sign Pattern of the Derivative
Explanation     Example A     Example B     Example C     Example D

Chapter 8:         Radical Functions
Chapter 8 Overview: Types and Traits of Radical Functions 
8-1:         Zeros and Domain   
Explanation     Example A     Example B&C     Example D     Example E
8-2:         The Chain Rule    
Explanation     Example A-B-C     Example D    Example E     Example F
8-3:         Extreme Points of Radical Functions 
Explanation     Example A     Example B     Example C     Example D
8-4:         General Radical Curve Sketching  
Explanation     Example A     Example B     Example C      Example D     Example E
8-5:         Implicit Differentiation     
Explanation     Example A     Example B     Example C     Example D
8-6:         Related Rates        
Explanation     Example A     Example B     Example C     Example D 
 

Chapter 9:         Piece-wise Defined Functions
Chapter 9 Overview: Continuity and Piece-wise Defined Functions
9-1:         One-Sided Limits    
Explanation     Example A     Example B&C&D    
9-2:         Continuity and Discontinuity
Explanation    Example A      Example B     Example C      Example D
9-3:         Differentiability and Smoothness
Explanation    Example A      Example B     Example C      Example D
9-4:         Sketching Piece-wise Defined Functions 
Explanation     Example A     Example B     Example C     


Chapter 10:         Exponential and Logarithmic Functions
Chapter 10 Overview: Types and Traits of Exponential and Logarithmic Functions                         
10-1:         Review of Exponential and Logarithmic Operations
Explanation     Examples A & B     Examples C & D     Example E
10-1:         Financial Applications  
Explanation     Example A     Example B     Example C     Example D
10-2:         VAs, Zeros, and Domains of Exponential and Log Functions
Explanation     Example A     Example B     Example C     Example D
10-3:         Limit and Derivative Rules 
Explanation     Example A     Example B     Example C     Example D
10-4:         The Product Rule  
Explanation     Example A     Example B     Example C     Example D
10-4:         Implicit Differentiation with the Product Rule  
Explanation     Example A     Example B     Example C & D  
10-5:         L'Hopital's Rule
Explanation     Example A     Example B     Example C      Example D     
10-6:         End Behavior
Explanation     Example A     Example B     Example C     Example D & E
10-7:         Exponential and Product Curve Sketching  
Explanation    Example A      Example B     Example C      Example D      Example E
10-8:         Logarithmic Curve Sketching
Explanation     Example A     Example B     Example C     Example D


Chapter 11:         General Trigonometric Functions
Chapter 11 Overview: Types and Traits of General Trigonometric Functions
11-1:         Review or Trigonometric Parent Functions
Explanation     Example A     Example B     Example C     Example D 
     Point-by-Point plotting of Sinusoidals 
11-2:         Trigonometric and Trig Inverse Derivatives with the Chain Rule  
Explanation     Example A     Example B     Example C     Example D
11-3:         The Product and Quotient Rules Revisited  
Explanation     Example A     Example B     Example C     Example D
11-4:         General Trigonometric Curve Sketching  

11-5:         Inverse Trigonometric Functions and Their Derivatives  
Explanation     Example A     Example B     Example C     Example D    



Chapter 12:         The Second Derivative
Chapter 12 Overview 
12-1:         Second Derivatives
Explanation     Example A     Example B     Example C     Example D    
12-1:         Concavity and Points of Inflection
Explanation     Example A     Example B     Example C     Example D
12-2:         The Second Derivative Test
Explanation     Example A     Example B     Example C     Example D
12-3:         Advanced Curve Sketching  
Explanation     Example A     Example B     Example C     Example D     Example E     Example F
12-4:         Graphical Analysis 
Explanation     Example A     Example B     Example C     Example D      Example E
      

Chapter 13:         Integrals
Chapter 13 Overview: The Integral
13-1:         Anti-Derivatives: The Power Rule   
Explanation     Example A     Example B     Example C     Example D
13-2:         Integration by Substitution: The Chain Rule  
Explanation     Example A     Example B     Example C     Example D
13-3:         Anti-Derivatives: The Transcendental Rules    
Explanation     Example A     Example B     Example C     Example D     Example E
13-4:         Definite Integrals        
Explanation     Example A     Example B     Example C     Example D
13-4:         Definite Integrals and Substitution      
Explanation     Example A     Example B     Example C     Example D
13-5:         Definite Integrals and Area  
Explanation     Example A     Example B     Example C     Example D