Houston Area Calculus Teachers HACT Feb 2022

Doug Kuhlmann, Feb 8, 2022

A collection of applets demonstrated on Feb 19, 2022 for the Houston Area Calculus Teachers by Doug Kuhlmann. All are best viewed in the GeoGebra app by opening from this site or downloading.

Table of Contents

  1. Derivatives
    1. Secant to tangent
    2. Derivative Plot
    3. Derivative Builder
    4. Copy of Zoom to tangent by Mike May
    5. Increasing/decreasing and f'(x)
    6. Concavity and f ' '(x)
    7. Explore increasing/decreasing & concavity
    8. Graph f(x) given f '(x)
  2. Riemann Integral
    1. Left, Right, Mid-point, Trap Sums
    2. Riemann Sums
    3. Random Riemann Sum
    4. Compares Mid-point and Trap. Which is closer?
    5. Error bounds (crude) for left, right decreasing
  3. Integral properties
    1. Integral from a to b to c
    2. Function as integral
    3. Function as integral with trig integrand
    4. Function as integral with jump discontinuities
  4. A few applications
    1. Slope fields
    2. Average value of a function
    3. Arc lenght of function
    4. Arc lenght of parametric curve
  5. BC topics
    1. Polar grapher
    2. Polar rectangular grapher
    3. Polar area
    4. Taylor polynomials
    5. Velocity vector with x- and y-components
    6. Velocity Acceleration vectors
    7. Integral Test for Series
  6. Volumes

1.

Derivatives

  • 1. Secant to tangent
  • 2. Derivative Plot
  • 3. Derivative Builder
  • 4. Copy of Zoom to tangent by Mike May
  • 5. Increasing/decreasing and f'(x)
  • 6. Concavity and f ' '(x)
  • 7. Explore increasing/decreasing & concavity
  • 8. Graph f(x) given f '(x)

1.1.

Secant to tangent

Make Δx smaller to move Q closer to P and secant line closer to tangent line. Best viewed in app.
– Doug Kuhlmann

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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2.

Riemann Integral

  • 1. Left, Right, Mid-point, Trap Sums
  • 2. Riemann Sums
  • 3. Random Riemann Sum
  • 4. Compares Mid-point and Trap. Which is closer?
  • 5. Error bounds (crude) for left, right decreasing

2.1.

Left, Right, Mid-point, Trap Sums

Riemann Sums for left, right, mid-pont and trapezoid rules.
– Doug Kuhlmann

2.2.

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2.3.

–

2.4.

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2.5.

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3.

Integral properties

  • 1. Integral from a to b to c
  • 2. Function as integral
  • 3. Function as integral with trig integrand
  • 4. Function as integral with jump discontinuities

3.1.

Integral from a to b to c

Theorem is true regardless of the order of a, b and c.
– Doug Kuhlmann

3.2.

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3.3.

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3.4.

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4.

A few applications

  • 1. Slope fields
  • 2. Average value of a function
  • 3. Arc lenght of function
  • 4. Arc lenght of parametric curve

4.1.

Slope fields

– Doug Kuhlmann

4.2.

–

4.3.

–

4.4.

–

5.

BC topics

  • 1. Polar grapher
  • 2. Polar rectangular grapher
  • 3. Polar area
  • 4. Taylor polynomials
  • 5. Velocity vector with x- and y-components
  • 6. Velocity Acceleration vectors
  • 7. Integral Test for Series

5.1.

Polar grapher

Can graph up to three polar graphs. All can be changed
– Doug Kuhlmann

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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6.

Volumes


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