Calculus Doug Kuhlmann

Doug Kuhlmann, Jun 25, 2014

A collection of applets that I use in my calculus classes.

Table of Contents

  1. Derivatives
    1. Derivative Plot
    2. Secant to Tangent Line
    3. Zoom to Tangent Window
    4. Derivative builder
  2. Integral calculus
    1. Riemann Sum
    2. Left, Right, Midpoint, Trap sums
    3. Random Riemann Sum
    4. Integral from a to b to c
    5. Function Defined via Integral
    6. Function as integral - 4 functions
    7. Average Value of a Function
    8. Left-Right Differences Incr/decr functions
    9. Arc Length y=f(x)
    10. Arc Length Parametric Curve
    11. Solids Of Revolution
  3. BC topics
    1. Slope Fields
    2. Taylor polynomial graphs
    3. Velocity vector with dx/dt, dy/dt components
    4. Integral Test for Series
    5. Polar Grapher
    6. Rectangular Polar Graphs
    7. Polar Area
    8. Velocity Acceleration Vectors on Parametric Curve
  4. Volumes--see book Volumes in Calculus and AP Volumes in Calculus

1.

Derivatives

  • 1. Derivative Plot
  • 2. Secant to Tangent Line
  • 3. Zoom to Tangent Window
  • 4. Derivative builder

1.1.

Derivative Plot

As A moves slope of tangent line is plotted. Move A along x-axis or use Animate button.
Derivative Plot
– Doug Kuhlmann

1.2.

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1.3.

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1.4.

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2.

Integral calculus

  • 1. Riemann Sum
  • 2. Left, Right, Midpoint, Trap sums
  • 3. Random Riemann Sum
  • 4. Integral from a to b to c
  • 5. Function Defined via Integral
  • 6. Function as integral - 4 functions
  • 7. Average Value of a Function
  • 8. Left-Right Differences Incr/decr functions
  • 9. Arc Length y=f(x)
  • 10. Arc Length Parametric Curve
  • 11. Solids Of Revolution

2.1.

Riemann Sum

Shows the value of an approximating Riemann sum and Trapepzoid sum also.

Change a and b by points along X-axis. Change n, the number of intervals, and p, the position in the interval where the function is evaluated by using the sliders
– Doug Kuhlmann

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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2.9.

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2.10.

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2.11.

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3.

BC topics

  • 1. Slope Fields
  • 2. Taylor polynomial graphs
  • 3. Velocity vector with dx/dt, dy/dt components
  • 4. Integral Test for Series
  • 5. Polar Grapher
  • 6. Rectangular Polar Graphs
  • 7. Polar Area
  • 8. Velocity Acceleration Vectors on Parametric Curve

3.1.

Slope Fields

Draws slope field for given dy/dx=f(x,y). Controls are in Graphics 2. Will also draw solutions through points that are added by user using the point tool.
Slope Fields
– Doug Kuhlmann

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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4.

Volumes--see book Volumes in Calculus and AP Volumes in Calculus


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