Interactive Calculus Activities
- Page ID
- 85500
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\dsum}{\displaystyle\sum\limits} \)
\( \newcommand{\dint}{\displaystyle\int\limits} \)
\( \newcommand{\dlim}{\displaystyle\lim\limits} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\(\newcommand{\longvect}{\overrightarrow}\)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\ket}[1]{\left| #1 \right>}\)
\(\newcommand{\bra}[1]{\left< #1 \right|}\)
\(\newcommand{\braket}[2]{\left< #1 \vphantom{#2} \right| \left. #2 \vphantom{#1} \right>}\)
\(\newcommand{\braopket}[3]{\left< #1 \vphantom{#2}\vphantom{#3} \right| #2 \vphantom{#1}\vphantom{#3} \left| #3 \vphantom{#1}\vphantom{#2} \right>}\)
\(\newcommand{\qmvec}[1]{\mathbf{\vec{#1}}}\)
\(\newcommand{\op}[1]{\hat{\mathbf{#1}}}\)
\(\newcommand{\expect}[1]{\langle #1 \rangle}\)
\(\newcommand{\dfn}[1]{\emph{\textbf{#1}}}\)
Below is a list of visualizations and activities that will help students learn calculus.
Pre-Calculus
- Absolute Value Inequalities
- Play the Linear Expressions Vocabulary Game
- Practice the Rules of Exponents
- Find the Slope of a Line By Measuring the Rise and the Run
- How Inverses are Sketched
Limits, Continuity, and Derivatives
- Tables and Limits
- Real World Continuity
- Epsilon Delta Limit Definition Activity
- Tangent Line Visualization
- Sketch the Graph of \(y = f'(x)\) given the graph of \(y = f(x)\)
- Calculus Properties Game
- Estimating \(f(a+h)\) using \(f(a) + f'(a)h\)
- Visually Approximating e
- Filming the Ingenuity Mars Helicopter Using Related Rates
- Differential, Error, and Relative Error Visualization
- Consultant for Max/Min Business
- The Mean Value Theorem Visualization
- Sketch the Graph of \(y = f''(x)\) given the graph of \(y = f(x)\)
- End Behavior Activity
- Visualize Newton's Method
Integration
- Shoot a Basketball Game
- Left and Right Endpoint Approximations
- Visualize the Average Value
- Pick the Speed to Win a Race Game
- Identify When a Tumor that is Growing Exponentially Will Reach a Certain Size
- Visualizing the Disk Method
- Visualizing the Washer Method 1
- Visualizing the Washer Method 2
- Visualizing the Washer Method 3
- Visualizing the Shell Method
- Visualizing Arc Length
- Fluid Force on Aquarium Window
- Center of Mass of a Teeter Totter
- Newton's Law of Cooling for Forensic Pathology
- Length of a Hyperbolic Cosine Shaped Bridge
- Integration by Parts Activity
- Integration Mathman
- Visualizing the Midpoint Rule
- Visualizing the Trapezoidal Rule
- Visualizing Simpson's Rule
- Integral Approximations
- Euler's Method Visualization
- Logistics Growth Model and the World Population
- Differential Equation Direction Fields
Sequences and Series
Multivariable Calculus
- Visualize a Parametric Curve As Time Elapses
- Multiple Petaled Roses Using Polar Coordinates
- Conic Sections in Polar Coordinates and Their Graphs
- Sketching a vector in 3D
- Cylindrical Surface Visualization
- Quadric Surfaces Visualization Activity
- Deciding Whether to Use a Dot Product, Cross Product, or Something Else to Solve a Problem
- Visualize Level Surfaces
- Limits of Multivariate Functions That Don't Exist
- Interactive Tangent Plane to a Surface Creator
- Visualizing a Surface and Its Gradient
- Watch the Tangent Vector of a Vector Valued Function Animate as \(t\) Increases
- Circle of Curvature
- Finding the Tangential and Normal Components of Acceleration for a Truck on a Road
- Visualizing the Definition of the Double Integral
- Matrix Transformations
They are meant to be embedded in the customized calculus textbook such as in the calculus links below:
- First Quarter Calculus Textbook, YouTube Videos Playlist
- Second Quarter Calculus Textbook, YouTube Videos Playlist
- Third Quarter Calculus Textbook, YouTube Videos Playlist
- Vector Calculus Textbook, YouTube Video Playlist


