Precalculus Spring Semester

Gary Rubinstein, Feb 15, 2018

Table of Contents

  1. Complex Numbers
    1. Rectangular To Trigonometric Form
    2. Angle and Length To Rectangular
    3. Complex Multiply
    4. Complex Multiply With Labels
    5. Multiply Complex Rule
    6. Geometric Proof Of Multiplication Rule
    7. Geometric Proof Of Multiplication Rule Activity
    8. Finding all n complex roots of an nth degree equation
    9. Nth Roots of a Complex Number
    10. Mandelbrot Iteration Orbits
    11. Mandelbrot Painter
    12. Mandelbrot set
    13. Mandelbrot Visualization
    14. Mandelbrot Orbit
  2. Polar Graphing
    1. Graphing Limaçons
    2. Graph Polar Functions
    3. Trisecting an angle with the Spiral of Archimedes
    4. Trisecting an angle with the Conchoid of Nicomedes
    5. Kappa Curve
    6. Cissoid Of Diocles
    7. Rectangular Polar Tracer
    8. Conchoid Of Nicomedes
  3. Conic Sections
    1. Tangent To A Parabola
    2. Descartes Tangent Method
    3. Parabola Locus
    4. Parabola Paper Folding
    5. Parabola Relationship Between p and a
    6. Ellipse Gardner's Construction
    7. Ellipse With Paper Folding
    8. Ellipse Focus Directrix Eccentricity
    9. Tangent To Ellipse
    10. Hyperbola Eccentricity
    11. Hyperbola Paper Folding
    12. Hyperbola Two Foci Definition
    13. General Focus Directrix For Conics
    14. Appolonius Parabola 2
    15. Quadratic equation solutions with a circle and a line
    16. Solving Quartics With A Parabola And A Circle
    17. Constructing solutions to quartic equations
    18. Sextic equation with six real roots
    19. Conic Sections
  4. Parametric Graphing
    1. Epicycloid example 1
    2. Epicycloid example 2
    3. Epicycloid example 3
    4. Epicycloid example 4
    5. Epicycloid Floating
    6. Epicycloid Rolling
    7. Parametric Grapher
    8. Cycloid-Like Curves
    9. Rolling Circle With Center On A Segment
    10. Epicycloid With Auxilliary Lines
    11. Cycloid Analysis
  5. Linear Algebra
    1. Using Matrices For Transformations
    2. Transformation With Matrices
    3. Visualizing Inverse Matrices
    4. Putting An Image Through A Linear Transformation
  6. Limits
    1. Riemann Sums
    2. Riemann Sums
    3. Riemann Sum

1.

Complex Numbers

  • 1. Rectangular To Trigonometric Form
  • 2. Angle and Length To Rectangular
  • 3. Complex Multiply
  • 4. Complex Multiply With Labels
  • 5. Multiply Complex Rule
  • 6. Geometric Proof Of Multiplication Rule
  • 7. Geometric Proof Of Multiplication Rule Activity
  • 8. Finding all n complex roots of an nth degree equation
  • 9. Nth Roots of a Complex Number
  • 10. Mandelbrot Iteration Orbits
  • 11. Mandelbrot Painter
  • 12. Mandelbrot set
  • 13. Mandelbrot Visualization
  • 14. Mandelbrot Orbit

1.1.

Rectangular To Trigonometric Form

– Gary Rubinstein

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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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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2.

Polar Graphing

  • 1. Graphing Limaçons
  • 2. Graph Polar Functions
  • 3. Trisecting an angle with the Spiral of Archimedes
  • 4. Trisecting an angle with the Conchoid of Nicomedes
  • 5. Kappa Curve
  • 6. Cissoid Of Diocles
  • 7. Rectangular Polar Tracer
  • 8. Conchoid Of Nicomedes

2.1.

Graphing Limaçons

You can drag the point [math]P[/math] on the rectangular graph.[br]Notice that the red portions of the graph correspond to negative [math]y[/math]-values on the rectangular graph, or negative [math]r[/math] values on the polar graph.
– Brian Sterr

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.

Conic Sections

  • 1. Tangent To A Parabola
  • 2. Descartes Tangent Method
  • 3. Parabola Locus
  • 4. Parabola Paper Folding
  • 5. Parabola Relationship Between p and a
  • 6. Ellipse Gardner's Construction
  • 7. Ellipse With Paper Folding
  • 8. Ellipse Focus Directrix Eccentricity
  • 9. Tangent To Ellipse
  • 10. Hyperbola Eccentricity
  • 11. Hyperbola Paper Folding
  • 12. Hyperbola Two Foci Definition
  • 13. General Focus Directrix For Conics
  • 14. Appolonius Parabola 2
  • 15. Quadratic equation solutions with a circle and a line
  • 16. Solving Quartics With A Parabola And A Circle
  • 17. Constructing solutions to quartic equations
  • 18. Sextic equation with six real roots
  • 19. Conic Sections

3.1.

Tangent To A Parabola

– Gary Rubinstein

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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3.12.

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3.13.

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3.14.

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3.15.

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3.16.

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3.17.

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3.18.

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3.19.

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4.

Parametric Graphing

  • 1. Epicycloid example 1
  • 2. Epicycloid example 2
  • 3. Epicycloid example 3
  • 4. Epicycloid example 4
  • 5. Epicycloid Floating
  • 6. Epicycloid Rolling
  • 7. Parametric Grapher
  • 8. Cycloid-Like Curves
  • 9. Rolling Circle With Center On A Segment
  • 10. Epicycloid With Auxilliary Lines
  • 11. Cycloid Analysis

4.1.

Epicycloid example 1

– Gary Rubinstein

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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5.

Linear Algebra

  • 1. Using Matrices For Transformations
  • 2. Transformation With Matrices
  • 3. Visualizing Inverse Matrices
  • 4. Putting An Image Through A Linear Transformation

5.1.

Using Matrices For Transformations

– Gary Rubinstein

5.2.

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5.3.

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5.4.

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6.

Limits

  • 1. Riemann Sums
  • 2. Riemann Sums
  • 3. Riemann Sum

6.1.

Riemann Sums

To approximate the area under a graph we split the region up into many thin rectangles. Drag the slider labeled n to increase the number of rectangles used.[br][br]The height of the approximating rectangle can be taken to be the height of the left endpoint, the height of the right endpoint, or the height of any point in the subinterval. Drag the slider labeled "position" to change the point used for the height of the rectangle.[br][br]The sum of the areas of all the thin rectangles is the Riemann Sum displayed.[br][br]If you wish to change the function f, say to sin(x), then just type f(x)=sin(x) in the input field at the bottom of the applet.
– Gary Rubinstein, J Mulholland

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6.3.

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