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
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