Calculus Applets

Chip Rollinson, Jun 25, 2014

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. limit of sin(h)/h as h goes to 0
    9. Calculus - Derivative of Sine (Geometric proof)
    10. Calculus - Newton's Method
    11. Calculus - The Derivative of an Inverse Function
    12. Derivative of the arctangent geometrically
    13. Calculus - Derivative of exponential functions f(x)=b^x
    14. GeoGebra Calculus Applets
    15. Calculus - Cone Inscribed In Sphere
    16. Calculus - Unit Sphere Inscribed In Cone
    17. Calculus - Ring of Spheres
    18. Viewing Angle (inverse trig derivatives)
    19. 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 proof exploration
    10. Cylindrical Shells
    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. Cut cylinder
    18. Torus Intersections
    19. Intersecting cylinders
    20. Calculus - Rotating y=a*sqrt(x-ax^2) about x=0
    21. Calculus - Arc Length
    22. Calculus - Surface Area
    23. Cube Cross Sections
  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.
    9. Phase Plane - Nonlinear System
  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. Alternating Series Illustrated
    5. Partial Sums Alternating Series
    6. Alternating Harmonic Series Sum
    7. Taylor Polynomials and Convergence
    8. Calculus - Taylor Inequality (LaGrange Error Bound)
    9. Series for pi/4 and pi^2/6
  6. Multivariable Calculus
    1. Partial derivatives (interactive geometric overview)
    2. Partial Derivatives: Graphical Illustrator
    3. Plane and elliptic paraboloid
    4. Plane and quadric surface
    5. 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. limit of sin(h)/h as h goes to 0
  • 9. Calculus - Derivative of Sine (Geometric proof)
  • 10. Calculus - Newton's Method
  • 11. Calculus - The Derivative of an Inverse Function
  • 12. Derivative of the arctangent geometrically
  • 13. Calculus - Derivative of exponential functions f(x)=b^x
  • 14. GeoGebra Calculus Applets
  • 15. Calculus - Cone Inscribed In Sphere
  • 16. Calculus - Unit Sphere Inscribed In Cone
  • 17. Calculus - Ring of Spheres
  • 18. Viewing Angle (inverse trig derivatives)
  • 19. Triangle formed by a hyperbola's tangent and asymptotes

1.1.

Calculus - Definition of the derivative

Definition of the derivative
– Chip Rollinson

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1.15.

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1.16.

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1.19.

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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 proof exploration
  • 10. Cylindrical Shells
  • 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. Cut cylinder
  • 18. Torus Intersections
  • 19. Intersecting cylinders
  • 20. Calculus - Rotating y=a*sqrt(x-ax^2) about x=0
  • 21. Calculus - Arc Length
  • 22. Calculus - Surface Area
  • 23. Cube Cross Sections

2.1.

Calculus - Riemann

– Chip Rollinson

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2.11.

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2.18.

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2.19.

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2.20.

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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.
  • 9. Phase Plane - Nonlinear System

3.1.

Calculus - Slope Field (Direction Fields)

Slope field generator with multiple solutions:
– Chip Rollinson

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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

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4.7.

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4.8.

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4.9.

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Series

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

5.1.

Calculus - Stacking Boxes

– Chip Rollinson

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5.3.

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5.5.

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5.6.

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5.7.

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5.8.

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5.9.

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6.

Multivariable Calculus

  • 1. Partial derivatives (interactive geometric overview)
  • 2. Partial Derivatives: Graphical Illustrator
  • 3. Plane and elliptic paraboloid
  • 4. Plane and quadric surface
  • 5. Double Integrals

6.1.

Partial derivatives (interactive geometric overview)

It is an update of this one https://www.geogebra.org/m/pxfuehwe
– Daniel Mentrard

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