Table of Contents

1. Preliminary Review Topics
   1. Pythagorean Trigonometric Identity (1)
   2. Trig ID Movie (II)
   3. Trig ID Movie (III)
   4. Exponential Functions: Graphs
   5. Logarithmic Functions: Graphs
   6. Logarithmic Action!
   7. Logarithmic Action (2)!
   8. Logarithmic Action (3)!
   9. Logarithmic Action (4)!
   10. Logarithmic Action (4)! V2
   11. Logarithmic Action (3: V2)
2. Limits & Continuity
   1. Limits: Introductory Questions
   2. One CRAZY Limit !!!
   3. CRAZY FUNCTION!!!
   4. A tool to explore delta-epsilon understandings.
   5. Cont in uity
   6. IVT Dynamic Illustrator
   7. Continuity Questions
   8. Vertical Asymptote (Defined as a Limit)
   9. Horizontal Asymptote (Defined as a Limit)
   10. One Special Limit
   11. One Special Limit (V2)
3. Derivatives: Introduction & Intuition
   1. Average Velocity
   2. Average to Instantaneous (Intro)
   3. Sketch the Derivative (Warm Up)
   4. Intuitive Derivative Graphing Exercise
   5. Intuitive Derivative Graphing Exercise: REVAMPED!!!
   6. Drawing Derivatives
   7. Constructing Graphs of Derivative Functions (Intuitively)
   8. Average Rate of Change Intervals
   9. Average Rate of Change of a Function: Dynamic Illustration
   10. Average to Instantaneous Rate of Change
   11. Average Rate of Change vs. Instantaneous Rate of Change
   12. Derivative Function: Without Words
   13. Derivatives (Intro)-1
   14. Derivatives (Intro)-2
   15. Graphing The Derivative of a Function
   16. 3-Way Color-Changing Derivative Grapher
   17. When does f'(x) = f(x)?
   18. Mean Value Theorem
   19. Mean Value Theorem (Without Words)
   20. Mean Value Theorem: Quick Intuitive Tests
   21. Which is f, f', f'' ?
   22. Which is f, f', f''? Part 2 !!!
   23. Create a Function: Calculus
   24. Descartes' View of Tangents: Quick Overview
   25. Fermat Calculus Insight
4. Derivatives of Special Functions & Differentiation Techniques
   1. Derivative of a Product
   2. Important Trig Limits
   3. Derivative of Sine & Cosine Functions (Quick Investigation)
   4. Derivative of Tangent Function (Investigation)
   5. Implicit Differentiation: Intro
   6. Folium of Descartes
   7. Implicit Differentiation (Quick Check)
   8. Derivative of Arcsine Function
   9. Derivative of Arccosine Function
   10. Derivative of Arctangent Function
   11. Derivatives of Inverse Functions
   12. Derivative of Natural Log Function
5. Related Rates & Linearization of Functions
   1. Related Rates (1)
   2. Related Rates (2)
   3. Falling Ladder !!!
   4. Related Rates (3)
   5. Related Rates: Adjustable Cone with dh/dt Constant
   6. Filling a Cone: dV/dt Constant versus dh/dt Constant
   7. Related Rates (Rolling Carts Problem)
   8. Linearization Illustrator (Calculus)
   9. Linearization Checker (Calculus)
   10. Newton's Method: Illustrated
6. Closed Interval Method & Optimization Problems
   1. Critical Numbers & Critical Points of Functions (Intro)
   2. The Closed Interval Method (Application Problem)
   3. Optimization: Area of a Rectangle
   4. Distance From Point to Graph
   5. Marginal Revenue, Cost, Profit: Analysis Problem 1
   6. Minimizing the Area of a Triangle
   7. Optimization Problem: Isosceles Triangle Circumscribed about a Circle
   8. Optimization - Box
   9. Maximizing Trapezoid Area
   10. Optimization Challenge 1
   11. Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
   12. Honeybee Population (Growth Rate Question)
   13. Oil Pipeline Optimization Problem
   14. Cylinder Inscribed Inside Sphere
   15. Cylinder Inscribed In Cone
   16. Sphere Inscribed Inside a Right Circular Cone
   17. Circle Optimization Challenge!
7. Riemann Sums; Indefinite and Definite Integrals
   1. Definite Integral Illustrator (I)
   2. Trapezoid: Area (I)
   3. Trapezoid: Area (2)
   4. Definite Integral Illustrator (II)
   5. Definite Integrals: Sum
   6. What Makes a Function Even?
   7. What Makes a Function Odd?
   8. Odd Functions: Another Look (Take 2)!
   9. Parabolic Segment: Archimedes Insight
   10. Accumulations
   11. All Sums (Riemann Sums)
8. Areas and Volumes; Solids of Revolution & Non-Revolution
   1. U-Substitution (Definite Integrals)
   2. Areas Between Curves (Intro)
   3. Area Between Curves
   4. Area Between 2 Curves
   5. Rotating Function Graphs about the xAxis within GeoGebra AR
   6. Surface of Revolution: GeoGebra Augmented Reality Template
   7. Rotating about X-AXIS: Creating Surfaces of Revolution in GGB AR
   8. Rotating about Y-AXIS: Creating Surfaces of Revolution in GGB AR
   9. How to Create Surfaces of Revolution in GeoGebra Augmented Reality
   10. Visualizing Volumes of Rotation
   11. Volume of Solid of Revolution about x-axis
   12. Disc Action!!!
   13. Disc Method: REVAMPED!
   14. Solids of Revolution (Discs)
   15. Custom Made Solid of Revolution
   16. Washer Action!!! (1)
   17. Washer Action !!! (2) - Calculus
   18. Washer Method: REVAMPED!
   19. Cylindrical Shells: REVAMPED!
   20. Cylindrical Shell Action!!! (1)
   21. Cylindrical Shell Action!!! (2)
   22. Calculus: Surface of Revolution formed by Rotating Area Between 2 Functions
   23. Arc Length to Surface of Revolution: Calculus
   24. Gabriel's Horn: Virtual Exploration in GeoGebra Augmented Reality
   25. Modifiable Solid: Isosceles Right Triangle Cross Sections Parallel to yAxis (VA)
   26. Modifiable Solid: Isosceles Right Triangle Cross Sections Parallel to yAxis (VB)
   27. Modifiable Solid: Equilateral Triangle Cross Sections Parallel to yAxis
   28. Toblerone Warm Up Modeling Question for Algebra, Geometry, AND Calculus!
   29. Modifiable Solid: Isosceles Triangle (Modifiable) Cross Sections Parallel to yAxis
   30. Modifiable Solid: Square Cross Sections Parallel to yAxis
   31. Modifiable Solid: Rectangular Cross Sections Parallel to yAxis
   32. Custom Solid: Changeable Rhombus Cross Section Parallel to yAxis
   33. Modifiable Solid: Isosceles Trapezoid Cross Sections Parallel to yAxis
   34. Modifiable Solid: Regular Pentagon Cross Sections Parallel to yAxis
   35. Modifiable Solid: Regular Hexagon Cross Sections Parallel to yAxis
   36. Modifiable Solid: Regular Heptagon Cross Sections Parallel to yAxis
   37. Modifiable Solid: Regular Octagonal Cross Sections Parallel to yAxis
   38. Modifiable Solid: Regular Nonagon Cross Sections Parallel to yAxis
   39. Modifiable Solid: Regular Decagon Cross Sections Parallel to yAxis
   40. Modifiable Solid: Semicircular Cross Sections Parallel to yAxis
   41. Modifiable Solid: Parabolic Cross Sections Parallel to yAxis
   42. Custom Solid: Elliptical Cross Sections Parallel to yAxis
   43. Solids Formed From Certain Cross Sections
   44. Parabola Around y-Axis
   45. Parabola Rotated Around y-Axis Wireframe
   46. Parabola Rotated Around x-Axis
   47. Parabola Rotated Around x-Axis
   48. Solids of Revolution: Around the x-Axis
   49. Solids of Revolution: Around the y-Axis
   50. Solids of Revolution: Around y=6
   51. Calculus Solids
   52. V. of Solid NOT of Revolution
   53. Cross-Sections Perpendicular to x-Axis: Squares
   54. Cross-Sections Perpendicular to x-Axis: Equilateral Triangle
   55. Cross-Sections Perpendicular to x-Axis: Right Triangles
   56. Cross-Sections Perpendicular to x-Axis: Rectangles
   57. Areas & Volumes: Culminating Activity
   58. Custom Solid: Cross Sections Parallel to yAxis are Quadrilaterals Always Similar to the Base
9. Average Value and Arc Length
   1. Average Value of a Function
   2. Arc Length (Calculus)
10. Integration Techniques
    1. Apex Section 6.1-Integration using substitution
    2. Sine & Cosine of a Sum: Discovery
    3. Partial Fraction Decomposition Calculator
11. Differential Equations
    1. Slope Field
    2. Copy of Slope Fields.
    3. Euler's Method
    4. Quiz: Writing Exponential Growth & Decay Functions
    5. Exponential Growth vs. Decay (Intro)
    6. Newton's Law of Cooling
    7. Logistic Growth Function
12. Sequences & Series
    1. Sequences (Dynamic Illustrator)
    2. Convergent or Divergent Series
    3. Sum of Infinite Geometric Series
    4. Partial Sums Alternating Series
    5. Integral Test for Series
    6. Taylor Polynomials
13. Parametric Equations
    1. Parametric Path on a Number Line
    2. Parametric Path
    3. Parametric Equations (I)
    4. Parametric Equations Grapher
    5. Parametric Equations: dy/dx (Ex 1)
    6. Cycloid Animation!
14. Polar Coordinates
    1. Trig Function Values (30 Degrees)
    2. Trig Function Values (45 Degrees)
    3. Trig Function Values (60 Degrees)
    4. Special Angles in Standard Position: Intro (V1)
    5. Special Angles in Standard Position: Intro (V2)
    6. Special Angles in Standard Position: Intro (V3)
    7. Polar Coordinates: Introduction
    8. Writing Equivalent Polar Coordinates: Quiz
    9. Polar Function Grapher
    10. Derivatives in Polar Coordintes
    11. Areas with Polar Coordinates
    12. Area Between 2 Polar Graphs
    13. Arc Length in Polar Coordintes
15. Multivariable Calculus Topics
    1. Plotting Points in 3D: Dynamic Illustrator
    2. 3D BATTLESHIP !!!
    3. Cylindrical Coordinates: Dynamic Illustrator
    4. Spherical Coordinates: Dynamic Illustrator
    5. Partial Derivatives: Graphical Illustrator
    6. Sphere Investigation
    7. Circular Paraboloid of Revolution
    8. Animation 111
    9. Special Spheroid Action: Locus Illustration
    10. Animation 112
    11. Special Hyperboloid of 1 Sheet as a Locus
    12. Special Hyperboloid of 2 Sheets as a Locus
    13. Catenoid