Calculus

Tim Brzezinski, 2016. 9. 22.

차례

  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
    26. Sketching Derivatives of Freehand Drawn Functions
    27. Blank Templates: Sketch Your Own Function and Derivative Graphs
    28. Derivatives of Freehand Drawn Functions (via Locus Tool)
    29. Open Middle: Circle Tangent to Line (1)
  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
    13. Open Middle Calculus Problem
    14. Tangent to Cubic: Open Middle Problem
  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. Norman Window: Modifiable Explorer
    4. Optimization: Area of a Rectangle
    5. Distance From Point to Graph
    6. Marginal Revenue, Cost, Profit: Analysis Problem 1
    7. Minimizing the Area of a Triangle
    8. Optimization Problem: Isosceles Triangle Circumscribed about a Circle
    9. Optimization - Box
    10. Maximizing Trapezoid Area
    11. Optimization Challenge 1
    12. Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
    13. Honeybee Population (Growth Rate Question)
    14. Oil Pipeline Optimization Problem
    15. Cylinder Inscribed Inside Sphere
    16. Cylinder Inscribed In Cone
    17. Sphere Inscribed Inside a Right Circular Cone
    18. 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. Open Middle: Definite Integral Problem
    7. Open Middle: Definite Integral Problem (2)
    8. What Makes a Function Even?
    9. What Makes a Function Odd?
    10. Odd Functions: Another Look (Take 2)!
    11. Parabolic Segment: Archimedes Insight
    12. Accumulations
    13. 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. Visualizing Volumes of Rotation
    8. Volume of Solid of Revolution about x-axis
    9. Disc Action!!!
    10. Disc Method: REVAMPED!
    11. Solids of Revolution (Discs)
    12. Custom Made Solid of Revolution
    13. Washer Action!!! (1)
    14. Washer Action !!! (2) - Calculus
    15. Washer Method: REVAMPED!
    16. Cylindrical Shells: REVAMPED!
    17. Cylindrical Shell Action!!! (1)
    18. Cylindrical Shell Action!!! (2)
    19. Calculus: Surface of Revolution formed by Rotating Area Between 2 Functions
    20. Arc Length to Surface of Revolution: Calculus
    21. Gabriel's Horn: Virtual Exploration in GeoGebra Augmented Reality
    22. Modifiable Solid: Isosceles Right Triangle Cross Sections Parallel to yAxis (VA)
    23. Modifiable Solid: Isosceles Right Triangle Cross Sections Parallel to yAxis (VB)
    24. Modifiable Solid: Equilateral Triangle Cross Sections Parallel to yAxis
    25. Toblerone Warm Up Modeling Question for Algebra, Geometry, AND Calculus!
    26. Building Surfaces with Cross Sections and Function Modeling
    27. Modifiable Solid: Isosceles Triangle (Modifiable) Cross Sections Parallel to yAxis
    28. Modifiable Solid: Square Cross Sections Parallel to yAxis
    29. Modifiable Solid: Rectangular Cross Sections Parallel to yAxis
    30. Custom Solid: Changeable Rhombus Cross Section Parallel to yAxis
    31. Modifiable Solid: Isosceles Trapezoid Cross Sections Parallel to yAxis
    32. Modifiable Solid: Regular Pentagon Cross Sections Parallel to yAxis
    33. Modifiable Solid: Regular Hexagon Cross Sections Parallel to yAxis
    34. Modifiable Solid: Regular Heptagon Cross Sections Parallel to yAxis
    35. Modifiable Solid: Regular Octagonal Cross Sections Parallel to yAxis
    36. Modifiable Solid: Regular Nonagon Cross Sections Parallel to yAxis
    37. Modifiable Solid: Regular Decagon Cross Sections Parallel to yAxis
    38. Modifiable Solid: Semicircular Cross Sections Parallel to yAxis
    39. Modifiable Solid: Parabolic Cross Sections Parallel to yAxis
    40. Custom Solid: Elliptical Cross Sections Parallel to yAxis
    41. Solids Formed From Certain Cross Sections
    42. Parabola Around y-Axis
    43. Parabola Rotated Around y-Axis Wireframe
    44. Parabola Rotated Around x-Axis
    45. Parabola Rotated Around x-Axis
    46. Solids of Revolution: Around the x-Axis
    47. Solids of Revolution: Around the y-Axis
    48. Solids of Revolution: Around y=6
    49. Calculus Solids
    50. V. of Solid NOT of Revolution
    51. Cross-Sections Perpendicular to x-Axis: Squares
    52. Cross-Sections Perpendicular to x-Axis: Equilateral Triangle
    53. Cross-Sections Perpendicular to x-Axis: Right Triangles
    54. Cross-Sections Perpendicular to x-Axis: Rectangles
    55. Areas & Volumes: Culminating Activity
    56. Custom Solid: Cross Sections Parallel to yAxis are Quadrilaterals Always Similar to the Base
    57. Surface with Square Cross Sections
  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. Plotting Points in 3 Space
    3. Writing Ordered Triples
    4. 3D BATTLESHIP !!!
    5. Cylindrical Coordinates: Dynamic Illustrator
    6. Spherical Coordinates: Dynamic Illustrator
    7. Partial Derivatives: Graphical Illustrator
    8. Sphere Investigation
    9. Circular Paraboloid of Revolution
    10. Animation 111
    11. Special Spheroid Action: Locus Illustration
    12. Animation 112
    13. Special Hyperboloid of 1 Sheet as a Locus
    14. Special Hyperboloid of 2 Sheets as a Locus
    15. Catenoid
    16. Crazy Slide!

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)

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1.6.

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1.7.

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1.9.

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1.10.

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1.11.

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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)

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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
  • 26. Sketching Derivatives of Freehand Drawn Functions
  • 27. Blank Templates: Sketch Your Own Function and Derivative Graphs
  • 28. Derivatives of Freehand Drawn Functions (via Locus Tool)
  • 29. Open Middle: Circle Tangent to Line (1)

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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
  • 13. Open Middle Calculus Problem
  • 14. Tangent to Cubic: Open Middle Problem

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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

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6.

Closed Interval Method & Optimization Problems

  • 1. Critical Numbers & Critical Points of Functions (Intro)
  • 2. The Closed Interval Method (Application Problem)
  • 3. Norman Window: Modifiable Explorer
  • 4. Optimization: Area of a Rectangle
  • 5. Distance From Point to Graph
  • 6. Marginal Revenue, Cost, Profit: Analysis Problem 1
  • 7. Minimizing the Area of a Triangle
  • 8. Optimization Problem: Isosceles Triangle Circumscribed about a Circle
  • 9. Optimization - Box
  • 10. Maximizing Trapezoid Area
  • 11. Optimization Challenge 1
  • 12. Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
  • 13. Honeybee Population (Growth Rate Question)
  • 14. Oil Pipeline Optimization Problem
  • 15. Cylinder Inscribed Inside Sphere
  • 16. Cylinder Inscribed In Cone
  • 17. Sphere Inscribed Inside a Right Circular Cone
  • 18. Circle Optimization Challenge!

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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. Open Middle: Definite Integral Problem
  • 7. Open Middle: Definite Integral Problem (2)
  • 8. What Makes a Function Even?
  • 9. What Makes a Function Odd?
  • 10. Odd Functions: Another Look (Take 2)!
  • 11. Parabolic Segment: Archimedes Insight
  • 12. Accumulations
  • 13. All Sums (Riemann Sums)

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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. Visualizing Volumes of Rotation
  • 8. Volume of Solid of Revolution about x-axis
  • 9. Disc Action!!!
  • 10. Disc Method: REVAMPED!
  • 11. Solids of Revolution (Discs)
  • 12. Custom Made Solid of Revolution
  • 13. Washer Action!!! (1)
  • 14. Washer Action !!! (2) - Calculus
  • 15. Washer Method: REVAMPED!
  • 16. Cylindrical Shells: REVAMPED!
  • 17. Cylindrical Shell Action!!! (1)
  • 18. Cylindrical Shell Action!!! (2)
  • 19. Calculus: Surface of Revolution formed by Rotating Area Between 2 Functions
  • 20. Arc Length to Surface of Revolution: Calculus
  • 21. Gabriel's Horn: Virtual Exploration in GeoGebra Augmented Reality
  • 22. Modifiable Solid: Isosceles Right Triangle Cross Sections Parallel to yAxis (VA)
  • 23. Modifiable Solid: Isosceles Right Triangle Cross Sections Parallel to yAxis (VB)
  • 24. Modifiable Solid: Equilateral Triangle Cross Sections Parallel to yAxis
  • 25. Toblerone Warm Up Modeling Question for Algebra, Geometry, AND Calculus!
  • 26. Building Surfaces with Cross Sections and Function Modeling
  • 27. Modifiable Solid: Isosceles Triangle (Modifiable) Cross Sections Parallel to yAxis
  • 28. Modifiable Solid: Square Cross Sections Parallel to yAxis
  • 29. Modifiable Solid: Rectangular Cross Sections Parallel to yAxis
  • 30. Custom Solid: Changeable Rhombus Cross Section Parallel to yAxis
  • 31. Modifiable Solid: Isosceles Trapezoid Cross Sections Parallel to yAxis
  • 32. Modifiable Solid: Regular Pentagon Cross Sections Parallel to yAxis
  • 33. Modifiable Solid: Regular Hexagon Cross Sections Parallel to yAxis
  • 34. Modifiable Solid: Regular Heptagon Cross Sections Parallel to yAxis
  • 35. Modifiable Solid: Regular Octagonal Cross Sections Parallel to yAxis
  • 36. Modifiable Solid: Regular Nonagon Cross Sections Parallel to yAxis
  • 37. Modifiable Solid: Regular Decagon Cross Sections Parallel to yAxis
  • 38. Modifiable Solid: Semicircular Cross Sections Parallel to yAxis
  • 39. Modifiable Solid: Parabolic Cross Sections Parallel to yAxis
  • 40. Custom Solid: Elliptical Cross Sections Parallel to yAxis
  • 41. Solids Formed From Certain Cross Sections
  • 42. Parabola Around y-Axis
  • 43. Parabola Rotated Around y-Axis Wireframe
  • 44. Parabola Rotated Around x-Axis
  • 45. Parabola Rotated Around x-Axis
  • 46. Solids of Revolution: Around the x-Axis
  • 47. Solids of Revolution: Around the y-Axis
  • 48. Solids of Revolution: Around y=6
  • 49. Calculus Solids
  • 50. V. of Solid NOT of Revolution
  • 51. Cross-Sections Perpendicular to x-Axis: Squares
  • 52. Cross-Sections Perpendicular to x-Axis: Equilateral Triangle
  • 53. Cross-Sections Perpendicular to x-Axis: Right Triangles
  • 54. Cross-Sections Perpendicular to x-Axis: Rectangles
  • 55. Areas & Volumes: Culminating Activity
  • 56. Custom Solid: Cross Sections Parallel to yAxis are Quadrilaterals Always Similar to the Base
  • 57. Surface with Square Cross Sections

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9.

Average Value and Arc Length

  • 1. Average Value of a Function
  • 2. Arc Length (Calculus)

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10.

Integration Techniques

  • 1. Apex Section 6.1-Integration using substitution
  • 2. Sine & Cosine of a Sum: Discovery
  • 3. Partial Fraction Decomposition Calculator

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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

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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

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Parametric Equations

Contains Parametric Equations Applets (Precalculus & Calculus)

  • 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!

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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

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15.

Multivariable Calculus Topics

  • 1. Plotting Points in 3D: Dynamic Illustrator
  • 2. Plotting Points in 3 Space
  • 3. Writing Ordered Triples
  • 4. 3D BATTLESHIP !!!
  • 5. Cylindrical Coordinates: Dynamic Illustrator
  • 6. Spherical Coordinates: Dynamic Illustrator
  • 7. Partial Derivatives: Graphical Illustrator
  • 8. Sphere Investigation
  • 9. Circular Paraboloid of Revolution
  • 10. Animation 111
  • 11. Special Spheroid Action: Locus Illustration
  • 12. Animation 112
  • 13. Special Hyperboloid of 1 Sheet as a Locus
  • 14. Special Hyperboloid of 2 Sheets as a Locus
  • 15. Catenoid
  • 16. Crazy Slide!

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15.9.

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15.10.

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15.11.

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15.12.

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15.13.

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15.14.

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15.16.

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정보