Calculus Applets using GeoGebra - Java Versions (See HTML 5 versions.)

This website is a project by Marc Renault, supported by Shippensburg University. My goal is to make a complete library of applets for Calculus I that are suitable for in-class demonstrations and/or student exploration. I have created these applets using GeoGebra, wonderful (free!) software for creating dynamic visualizations of mathematical ideas.

All of these applets also appear in HTML 5 format.

Limits

  1. Intuitive Notion of the Limit
  2. Intuitive Notion of the Limit - One-Sided Limits
  3. The Limit Laws
  4. Continuity at a Point
  5. An Important Trig Limit `lim_(theta-->0) (sin(theta))/theta = 1`
  6. Average and Instantaneous Rate of Change

Differentiation

  1. The Derivative at a Point
  2. The Derivative as a Function
  3. The Derivative of Elementary Functions
  4. Try to Graph the Derivative Function
  5. The Derivative of Exponential Functions
  6. Identify the Derivative Function
  7. Derivatives and Graph Transformations
  8. Identify a Function and its First and Second Derivatives
  9. Identify an Antiderivative Function
  10. The Power Rule - Derivatives of Polynomial Functions
  11. Intuitive Notion of the Chain Rule
  12. Implicit Differentiation
  13. Derivatives of Inverse Functions

Applications of the Derivative

  1. First derivative test - Reconstruct `f` from its First Derivative
  2. Second derivative test - Reconstruct `f` from its Second Derivative
  3. Derivatives and the Shape of a Graph
  4. Related Rates Problems: Oil Slick -- A Falling Ladder -- A Conical Tank -- Driving Car -- Lamppost -- Two Trains -- Searchlight -- Rocket Launch
  5. Optimization Problems: Bending a Wire -- Rectangle Inscribed in a Parabola -- Three Pens -- Getting Power to an Island -- Another Wire Problem -- Function and Rectangle 1 -- Function and Rectangle 2 -- Triangle Circumscribing a Circle --

The Integral

  1. Introduction to Integration - The Exercise Bicycle Problem:   Part 1     Part 2
  2. Introduction to Integration - Gaining Geometric Intuition
  3. The Riemann Sum
  4. The Area Function
  5. The Fundamental Theorem of Calculus, Part I (Theoretical Part)
  6. The Fundamental Theorem of Calculus, Part II (Practical Part)

Additional Resources



Creative Commons License
Calculus Applets using GeoGebra by Marc Renault is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

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