MA443

Whan Ki Lee, Jan 20, 2017

Cal III

Table of Contents

  1. Chapter 10. Polar Coordinates
    1. Parametric Equations Grapher
    2. The Cycloid
    3. Graphing in Polar Coordinates
    4. Polar rose
    5. Area of a region using a polar coordinate system
    6. Area Between 2 Polar Graphs
  2. Chapter 12. Vectors and the Geometry of Space
    1. Vector operations
    2. Vector Equation of a line 3D
    3. Normal Vector and Plane
    4. 11.5 Distance between a point and a plane
    5. General Quadric Surface
    6. Cross Product Applications
    7. The Cross Product
    8. Level Curve
  3. Chapter 13. Vector Functions
    1. Interpreting Curvature
    2. Curvature
    3. TNB frame
  4. Chapter 14. Partial Derivatives
    1. Illustrating Partial Derivatives
    2. Visualizing level curves
    3. Tangent Plane to a Surface
    4. Tangent Plane
    5. Gradient Vector
    6. Gradient vs. Level Curves
    7. Directional derivatives and Gradient
    8. Min-Max-Saddle Example
    9. Visualizing the Lagrange Multiplier Method.
    10. A Dynamic View of Lagrange Multipliers
    11. Monkey Saddle
    12. Lagrange Multiplier Method - Example
  5. Chapter 15 Multiple Integrals
    1. Definition of the double integral
    2. Fubini's theorem

1.

Chapter 10. Polar Coordinates

10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Equations 10.3 Polar Coordinates 10.4 Areas and Lengths in Polar Coordinates

  • 1. Parametric Equations Grapher
  • 2. The Cycloid
  • 3. Graphing in Polar Coordinates
  • 4. Polar rose
  • 5. Area of a region using a polar coordinate system
  • 6. Area Between 2 Polar Graphs

1.1.

Parametric Equations Grapher

– Tim Brzezinski

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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2.

Chapter 12. Vectors and the Geometry of Space

  • 1. Vector operations
  • 2. Vector Equation of a line 3D
  • 3. Normal Vector and Plane
  • 4. 11.5 Distance between a point and a plane
  • 5. General Quadric Surface
  • 6. Cross Product Applications
  • 7. The Cross Product
  • 8. Level Curve

2.1.

Vector operations

– David Richeson

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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3.

Chapter 13. Vector Functions

  • 1. Interpreting Curvature
  • 2. Curvature
  • 3. TNB frame

3.1.

Interpreting Curvature

For a circle of radius r, the curvature at any point is k = 1/r. One way of interpreting curvature is to think of it as the rate at which the unit tangent vector is changing direction with respect to the arc length parameter. As the radius of the circle increases, the curvature decreases and so does the rate at which the unit tangent vector changes direction.
– Chris Mizell

3.2.

–

3.3.

–

4.

Chapter 14. Partial Derivatives

  • 1. Illustrating Partial Derivatives
  • 2. Visualizing level curves
  • 3. Tangent Plane to a Surface
  • 4. Tangent Plane
  • 5. Gradient Vector
  • 6. Gradient vs. Level Curves
  • 7. Directional derivatives and Gradient
  • 8. Min-Max-Saddle Example
  • 9. Visualizing the Lagrange Multiplier Method.
  • 10. A Dynamic View of Lagrange Multipliers
  • 11. Monkey Saddle
  • 12. Lagrange Multiplier Method - Example

4.1.

Illustrating Partial Derivatives

Illustrating the concept of partial derivatives using the function [math]f(x,y) = sin(x) + cos(y)[/math].[br]Drag point A (the [color=#00FF00]GREEN[/color] point)
– Steve Phelps

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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4.10.

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4.11.

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4.12.

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5.

Chapter 15 Multiple Integrals

  • 1. Definition of the double integral
  • 2. Fubini's theorem

5.1.

Definition of the double integral

– Joseph Manthey

5.2.

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