Calculus Applets

Chip Rollinson, Doug Kuhlmann, Nov 1, 2022

Here are a bunch of Single Variable Calculus applets. I'll be adding more as I make them or find them.

Table of Contents

  1. Derivatives
    1. Calculus - Definition of the derivative
    2. Calculus - Tangent Zoom
    3. 3-Way Color-Changing Derivative Grapher
    4. Derivative Function: Without Words
    5. Try to Graph the Derivative Function
    6. Related Rates - Spinning Laser
    7. Calculus - Mean Value Theorem (MVT)
    8. Calculus - Derivative of Sine (Geometric proof)
    9. Calculus - Newton's Method
    10. Calculus - The Derivative of an Inverse Function
    11. Derivative of the arctangent geometrically
    12. Calculus - Derivative of exponential functions f(x)=b^x
    13. GeoGebra Calculus Applets
    14. Calculus - Cone Inscribed In Sphere
    15. Calculus - Unit Sphere Inscribed In Cone
    16. Calculus - Ring of Spheres
    17. Viewing Angle (inverse trig derivatives)
    18. Triangle formed by a hyperbola's tangent and asymptotes
  2. Integrals
    1. Calculus - Riemann
    2. Calculus - Reimann Sums vs. Trapezoids
    3. Calculus - Fundamental Theorem of Calculus
    4. FTC Playground3
    5. GeoGebra Calculus Applets
    6. Calculus - Average Value of a Function
    7. Disk/washer method for finding volume of solid of revolution
    8. Calculus - Washer Method
    9. Cylindrical Shells
    10. Cylindrical Shell Action!!! (2)
    11. Calculus - Pyramid
    12. Calculus - Known Cross Sections
    13. Solids with given cross sections
    14. Pond volume (AP Calculus 2008 FRQ #1d)
    15. Rotated Square Slices About a Line
    16. Visualizing volumes by known cross section
    17. 1/sqrt(x) rotated about x-axis
    18. Cut cylinder
    19. Torus Intersections
    20. Intersecting cylinders
    21. Calculus - Rotating y=a*sqrt(x-ax^2) about x=0
    22. Calculus - Arc Length
    23. Calculus - Surface Area
    24. Removing the "Hole"
  3. Differential Equations
    1. Calculus - Slope Field (Direction Fields)
    2. Calculus - Euler's Method
    3. Euler's Method Lab
    4. Calculus - Exponential vs. Logistic functions
    5. Logistic Examples
    6. dy/dx = 2y/x
    7. Calculus - Differential Equations - Virus Simulation
    8. Solution of a 1st order differential equation with slope field.
  4. Polar/Parametric (Vectors)
    1. Parametric Curves
    2. Vector Addition
    3. Parametric Functions - Velocity and Acceleration Vectors
    4. Parametric Area
    5. Polar vs Cartesian Functions
    6. Polar curves
    7. Calculus - Polar Area
    8. Zooming r=e^theta
    9. Goat Tethered to Silo
  5. Series
    1. Calculus - Stacking Boxes
    2. Calculus - Integral Test
    3. The Alternating Harmonic Series
    4. Partial Sums Alternating Series
    5. Alternating Harmonic Series Sum
    6. Calculus - Taylor Inequality (LaGrange Error Bound)
    7. Series for pi/4 and pi^2/6
  6. Multivariable Calculus
    1. Plane and elliptic paraboloid
    2. Plane and quadric surface
    3. Double Integrals

1.

Derivatives

  • 1. Calculus - Definition of the derivative
  • 2. Calculus - Tangent Zoom
  • 3. 3-Way Color-Changing Derivative Grapher
  • 4. Derivative Function: Without Words
  • 5. Try to Graph the Derivative Function
  • 6. Related Rates - Spinning Laser
  • 7. Calculus - Mean Value Theorem (MVT)
  • 8. Calculus - Derivative of Sine (Geometric proof)
  • 9. Calculus - Newton's Method
  • 10. Calculus - The Derivative of an Inverse Function
  • 11. Derivative of the arctangent geometrically
  • 12. Calculus - Derivative of exponential functions f(x)=b^x
  • 13. GeoGebra Calculus Applets
  • 14. Calculus - Cone Inscribed In Sphere
  • 15. Calculus - Unit Sphere Inscribed In Cone
  • 16. Calculus - Ring of Spheres
  • 17. Viewing Angle (inverse trig derivatives)
  • 18. Triangle formed by a hyperbola's tangent and asymptotes

1.1.

Calculus - Definition of the derivative

Definition of the derivative
– Chip Rollinson

1.2.

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1.3.

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1.4.

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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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1.15.

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1.16.

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1.17.

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1.18.

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2.

Integrals

  • 1. Calculus - Riemann
  • 2. Calculus - Reimann Sums vs. Trapezoids
  • 3. Calculus - Fundamental Theorem of Calculus
  • 4. FTC Playground3
  • 5. GeoGebra Calculus Applets
  • 6. Calculus - Average Value of a Function
  • 7. Disk/washer method for finding volume of solid of revolution
  • 8. Calculus - Washer Method
  • 9. Cylindrical Shells
  • 10. Cylindrical Shell Action!!! (2)
  • 11. Calculus - Pyramid
  • 12. Calculus - Known Cross Sections
  • 13. Solids with given cross sections
  • 14. Pond volume (AP Calculus 2008 FRQ #1d)
  • 15. Rotated Square Slices About a Line
  • 16. Visualizing volumes by known cross section
  • 17. 1/sqrt(x) rotated about x-axis
  • 18. Cut cylinder
  • 19. Torus Intersections
  • 20. Intersecting cylinders
  • 21. Calculus - Rotating y=a*sqrt(x-ax^2) about x=0
  • 22. Calculus - Arc Length
  • 23. Calculus - Surface Area
  • 24. Removing the "Hole"

2.1.

Calculus - Riemann

– Chip Rollinson

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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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2.12.

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2.13.

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2.14.

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2.15.

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2.16.

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2.17.

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2.18.

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2.19.

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2.20.

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2.21.

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2.22.

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2.23.

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2.24.

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3.

Differential Equations

  • 1. Calculus - Slope Field (Direction Fields)
  • 2. Calculus - Euler's Method
  • 3. Euler's Method Lab
  • 4. Calculus - Exponential vs. Logistic functions
  • 5. Logistic Examples
  • 6. dy/dx = 2y/x
  • 7. Calculus - Differential Equations - Virus Simulation
  • 8. Solution of a 1st order differential equation with slope field.

3.1.

Calculus - Slope Field (Direction Fields)

Slope field generator with multiple solutions:
– Chip Rollinson

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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.

Polar/Parametric (Vectors)

  • 1. Parametric Curves
  • 2. Vector Addition
  • 3. Parametric Functions - Velocity and Acceleration Vectors
  • 4. Parametric Area
  • 5. Polar vs Cartesian Functions
  • 6. Polar curves
  • 7. Calculus - Polar Area
  • 8. Zooming r=e^theta
  • 9. Goat Tethered to Silo

4.1.

Parametric Curves

This applet illustrates graphing parametric curves.
Parametric Curves
– gabriela sanchis

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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5.

Series

  • 1. Calculus - Stacking Boxes
  • 2. Calculus - Integral Test
  • 3. The Alternating Harmonic Series
  • 4. Partial Sums Alternating Series
  • 5. Alternating Harmonic Series Sum
  • 6. Calculus - Taylor Inequality (LaGrange Error Bound)
  • 7. Series for pi/4 and pi^2/6

5.1.

Calculus - Stacking Boxes

– Chip Rollinson

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.

Multivariable Calculus

  • 1. Plane and elliptic paraboloid
  • 2. Plane and quadric surface
  • 3. Double Integrals

6.1.

Plane and elliptic paraboloid

– Chip Rollinson

6.2.

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6.3.

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Information