This is a list of interactive applets, sorted by topic. The Calculus applets are organized by section number of the online textbook “Active Calculus” by Matt Boelkins.

This list exists mainly for archival purposes - all these links are also integrated on their corresponding topic pages, which you can also find by searching for the tag “interactive”.

Many of the listed applets are created by Marc Renault, otherwise a specific credit is noted.

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Calculus I

1.1 Velocity

• Average and Instantaneous Rate of Change (appears here)

1.2 Notion Of Limit

• Intuitive Notion of the Limit (appears here)

• Intuitive Notion of the Limit - One-Sided Limits (appears here)

1.3 Derivative At A Point

• The Derivative at a Point (appears here)

1.4 Derivative Function

• The Derivative as a Function (appears here)

• Try to Graph the Derivative Function (appears here)

• Identify the Derivative Function (appears here)

• Derivatives and Graph Transformations (appears here)

• Identify an Antiderivative Function (appears here)

1.5 Using The Derivative

1.6 Second Derivative

• Identify a Function and its First and Second Derivatives (appears here)

1.7 Limit Laws And Continuity

• The Limit Laws (appears here)
• Continuity at a Point (appears here)

1.8 Differentiability And Linearization

2.1 Basic Derivative Rules

• The Power Rule - Derivatives of Polynomial Functions (appears here)

• The Derivative of Exponential Functions (appears here)

2.2 Sine And Cosine

• An Important Trig Limit \(\displaystyle \lim_{\theta\to 0} \frac{\sin(\theta)}{\theta} = 1\) (appears here)

• The Derivative of Elementary Functions (appears here)

2.3 Product And Quotient Rules

2.4 Other Trig Functions

2.5 Chain Rule

• Intuitive Notion of the Chain Rule (appears here)

2.6 Inverse Functions

• Derivatives of Inverse Functions (appears here)

2.7 Implicit Differentiation

• Implicit Differentiation (appears here)

2.7b Logarithmic Differentiation

2.8 Hospitals Rule

2.9 More On Limits

3.1 Extreme Values

• First derivative test - Reconstruct \(f\) from its First Derivative (appears here)
• Second derivative test - Reconstruct \(f\) from its Second Derivative (appears here)
• Derivatives and the Shape of a Graph (appears here)

3.2 Families Of Functions

3.3a Global Optimization

3.3b Analysis Theorems

• Intermediate Value Theorem (by Philip Walker) (appears here)

• Mean Value Theorem:

  • https://www.geogebra.org/m/EE6nAgGC (loghind) (appears here)
  • https://www.geogebra.org/m/aajVcC9u (MrQuinn) (appears here)
  • https://www.geogebra.org/m/QHJJQX99 (MrQuinn) (appears here)

3.4 Applied Optimization

• Optimization Problems:
  • Bending a Wire (appears here)
  • Rectangle Inscribed in a Parabola (appears here)
  • Three Pens (appears here)
  • Getting Power to an Island (appears here)
  • Another Wire Problem (appears here)
  • Function and Rectangle 1 (appears here)
  • Function and Rectangle 2 (appears here)
  • Triangle Circumscribing a Circle (appears here)

3.5 Related Rates

• Related Rates Problems:
  • Oil Slick (appears here)
  • A Falling Ladder (appears here)
  • A Conical Tank (appears here)
  • Driving Car (appears here)
  • Lamppost (appears here)
  • Two Trains (appears here)
  • Searchlight (appears here)
  • Rocket Launch (appears here)

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Calculus II

8.1 Sequences

• Comparing a sequence with the graph of the corresponding function (by Tim Brzezinski) (appears here)

• Arithmetic Sequences (by nnhsmath) (appears here)

• Arithmetic Sequence Practice: Predicting future terms when the first 4 are shown (by nnhsmath) (appears here)

• Dynamic Sequences (beckykwarren) (appears here)

8.1b Review Of Limit Methods

8.2 Geometric Series

• Seeing Geometric Sequences (by Tom Owsiak) (appears here)

• Geometric Sequence Find the General Term Given Two Terms (by Aileen Fisher) (appears here)

8.3 General Series

• Plotting sequences (and also the corresponding partial sums) (by melbapplets) (appears here)

8.4 Alternating Series

8.5a Taylor Polyomials

8.5b Taylor Series

4.1 Determining Distance From Velocity

• Introduction to Integration - The Exercise Bicycle Problem:
  • Part 1 (appears here)
  • Part 2 (appears here)

4.2 Riemann Sums

• The Riemann Sum (appears here)

4.3 The Definite Integral

• Introduction to Integration - Gaining Geometric Intuition (appears here)

4.4 The Fundamental Theorem Of Calculus

5.1 Constructing Accurate Graphs of Antiderivatives

• Identify an Antiderivative Function (appears here)

5.2 Area Functions And The 2nd FTC

• The Area Function (appears here)

• The Fundamental Theorem of Calculus, Part I (Theoretical Part) (appears here)

• The Fundamental Theorem of Calculus, Part II (Practical Part) (appears here)

• 2nd Fundamental Theorem of Calculus (by John Holden) (appears here)

5.3 Substitution

5.4 Integration By Parts

5.5a Partial Fractions

5.5b Trigonometric Integrals

5.5c Trig Substitution

5.5d Tables And Computer Algebra Systems

5.6 8.6 Numerical Integration And Series

6.1 Area And Arclength

6.2a Volumes Discs

• Shodor Solids of Revolution (very flexible online visualization) (appears here)

• Wolfram Alpha Volume Calculator (by Wolfram Alpha, does the calculation but also shows a picture) (appears here)

• Wireframe interactive demo, using handdrawn curve (by selim_tezel) (appears here)

• Paul’s Online Math Notes: Volume with Rings (appears here)

• Wolfram Demonstrations Project: Solid of Revolution (You may be asked to download a plug-in – go ahead! It’s worth it.) (appears here)

6.2b Volumes Shells

6.3 Density And Mass

6.4 Work Force Pressure

6.5 Improper Integrals

7.1 Intro To Differential Equations

7.2-7.3 Slope Fields And Eulers Method

• Slope Fields (by Nestor Valles-Villarreal) (appears here)

7.4 Separable Differential Equations

9.1 Common Functions in Economics

9.2 Marginal Functions

• Cost and Marginal Cost (by Alex Kemphaus) (appears here)

9.3 Elasticity of Demand

• Total Revenue and Price Elasticity (by Yung Lee, needs work, in particular fix typo: “gain due to higher demand“) (appears here)

9.4 Gini Index, Consumer & Producer Surplus

• Gini index (by David Gurney) (appears here)
• Discrete Consumer Surplus (by David Beydler) (appears here)

• Continuous Consumer surplus (by David Beydler) (appears here)

• Total surplus (linear demand & supply) (by Joel Hammer) (appears here)

9.5 Future and Present Value of Continuous Income Streams

• Continous Income Stream (by Claire Blackman) (appears here)

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Linear Algebra

Parametric equations of lines and planes

• Parametrization of a line in \(\mathbb{R}^3\): https://www.desmos.com/3d/uqr7qigep4 (by Gabriel Indurskis) (appears here)
• Parametrization of a plane in \(\mathbb{R}^3\): https://www.desmos.com/3d/axvgyjyklf (by Gabriel Indurskis) (appears here)

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Additional Resources

• The GeoGebra website
• A GeoGebra tutorial
• Panning and zooming in GeoGebra applets
• https://www.gvsu.edu/math/videos-and-applets-54.htm (by the Dept. of Mathematics at Grand Valley State University)

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