Mathematica Activities

Mathematica
Activities
IMSA Math Team

Below are several Mathematica notebooks for you to download and use. There's a wide range of notebooks: simple demos, interactive demos, classroom activities, an introductory tutorial, and even a small palette for general use. These notebooks also vary by the amount of Mathematica experience they expect, but none require extensive knowledge of the software.

Tutorials and other stuff

1Tutorial.nb A short, introductory notebook to get you started. This is not intended to give much depth or independence in Mathematica, but it will allow you to use the other notebooks on this page.

2Tutorial.nb Only somewhat cleverly named, this is the second part of the short tutorial, but that's somewhat misleading. This introduces the Help system as well as the writing and formatting of notebooks. The section on getting help is appropriate after 1Tutorial.nb, but more background will help before trying to write (good) notebooks. If you're already comfortable with Mathematica, this notebook may be used independently, helping to teach you how to create notebooks of your own for student use.

full set of tutorials This will take you to a full set of in-depth IMSA Mathematica tutorials that start on page 1 and don't skip pages. (Find these near the bottom of the linked page.) These expect a good understanding of Algebra 2 and they may be used by students or teachers. Do as many of these tutorials as you wish.

IMSABasic.nb This is a small palette which includes commands for simplifying, defining functions, plotting functions, and other such things. To use this palette, on your hard drive, find the following folders and subfolders: Mathematica Files ->System Files ->Front End -> Palettes. Place the palette notebook in this Palettes folder. Open and use this palette as you open other palettes.

Demos (and more!)
These may be done by the teacher or used by students.

SineAnimation.nb An animation to show the sine graph as the angle moves around a unit circle.

CoSineAnimation.nb An animation to show the cosine graph as the angle moves around a unit circle.

TanAnimation.nb An animation to show the tangent graph is constructed as the angle moves around a unit circle.

RatsGrapher.nb Enter the numerator, denominator, and a window. The notebook plots the rational function, showing and labeling all asymptotes and holes.

Cobweb.nb This notebook includes several examples of cobweb diagrams and encourages exploration.

LimaçonAnim.nb An animation of polar graphs with equations of the form r = a + bcos(q) to show the relationships between limaçons and circles.

Zoom.nb Input a function, an x-value, and a starting interval. Then zoom in as desired. This gives graphical as well as numerical views.

CreatingDerivative.nb Enter a function, an interval, and a step size. An animation to show tangent lines and plot the value of the derivative at steps throughout the interval.

ConcavityDemo.nb Enter a function and view concavity as changes in the first derivative as an animation.

SeeingSeries.nb Input the k^th term of a series and a starting value. See the geometrical pattern of convergence for alternating series or series with all positive terms. Guess convergence or divergence from the geometry shown. Values for S_n are also given.

RandomRiemann.nb Choose a function, an interval, and a number of subintervals. Show a randomly created Riemann Sum over the interval.

Accumulator.nb Choose a function and then animate the plotting of the function and its integral.

V&AVectorsAnim.nb An animation to show the velocity and acceleration vectors as a point travels around a parametrically defined curve.

Activities for the Classroom

PolarPatterns.nb

PolarPatternsNew.nb These notebooks allow students to explore the graphs of basic polar equations. They are quite similar, varying only in the amount of Mathematica assumed. The "New" version is for new users with no previous experience with the software. (Note: Neither version assumes very much!)

Sequences.nb This allows students to look at values of sequences and then plots their values to help see patterns, convergence, and divergence. Some examples are given, and then students are asked to enter their own examples and explore on their own. (This requires very, very little knowledge of Mathematica.)

PowerDerivs.nb Use the definition of a derivative while Mathematica does the algebra to explore the power rule for differentiating functions.

Derivb^x.nb

Derivb^x.pdf A notebook to help make sense of the derivative of exponential functions of the form y = b^x and a pdf document to complement the file. (Give students a place to write what they've just done on the computer!)

Trig(kx).nb

Trig(kx).pdf A notebook and complementary pdf file to see the effects of k in the derivatives of y = sin(kx) and y = cos(kx). This is a small beginning to the chain rule and makes students review periods and amplitudes. (This assumes knowledge of the derivatives of the Sine and Cosine functions.)

x^ksin(x^(-1)).nb A notebook to help students look at the continuity and differentiability of functions of the form f(x) = x^k*sin(1/x) at the point x = 0. This expects some basic knowledge of Mathematica and asks students to type some complete commands by themselves.

Questions and comments? Contact Ruth.

Back to IMSA Mathematics Home Page.

Tutorials and other stuff
1Tutorial.nb	A short, introductory notebook to get you started. This is not intended to give much depth or independence in Mathematica, but it will allow you to use the other notebooks on this page.
2Tutorial.nb	Only somewhat cleverly named, this is the second part of the short tutorial, but that's somewhat misleading. This introduces the Help system as well as the writing and formatting of notebooks. The section on getting help is appropriate after 1Tutorial.nb, but more background will help before trying to write (good) notebooks. If you're already comfortable with Mathematica, this notebook may be used independently, helping to teach you how to create notebooks of your own for student use.
full set of tutorials	This will take you to a full set of in-depth IMSA Mathematica tutorials that start on page 1 and don't skip pages. (Find these near the bottom of the linked page.) These expect a good understanding of Algebra 2 and they may be used by students or teachers. Do as many of these tutorials as you wish.
IMSABasic.nb	This is a small palette which includes commands for simplifying, defining functions, plotting functions, and other such things. To use this palette, on your hard drive, find the following folders and subfolders: Mathematica Files ->System Files ->Front End -> Palettes. Place the palette notebook in this Palettes folder. Open and use this palette as you open other palettes.
Demos (and more!) These may be done by the teacher or used by students.
SineAnimation.nb	An animation to show the sine graph as the angle moves around a unit circle.
CoSineAnimation.nb	An animation to show the cosine graph as the angle moves around a unit circle.
TanAnimation.nb	An animation to show the tangent graph is constructed as the angle moves around a unit circle.
RatsGrapher.nb	Enter the numerator, denominator, and a window. The notebook plots the rational function, showing and labeling all asymptotes and holes.
Cobweb.nb	This notebook includes several examples of cobweb diagrams and encourages exploration.
LimaçonAnim.nb	An animation of polar graphs with equations of the form r = a + bcos(q) to show the relationships between limaçons and circles.
Zoom.nb	Input a function, an x-value, and a starting interval. Then zoom in as desired. This gives graphical as well as numerical views.
CreatingDerivative.nb	Enter a function, an interval, and a step size. An animation to show tangent lines and plot the value of the derivative at steps throughout the interval.
ConcavityDemo.nb	Enter a function and view concavity as changes in the first derivative as an animation.
SeeingSeries.nb	Input the k^th term of a series and a starting value. See the geometrical pattern of convergence for alternating series or series with all positive terms. Guess convergence or divergence from the geometry shown. Values for S_n are also given.
RandomRiemann.nb	Choose a function, an interval, and a number of subintervals. Show a randomly created Riemann Sum over the interval.
Accumulator.nb	Choose a function and then animate the plotting of the function and its integral.
V&AVectorsAnim.nb	An animation to show the velocity and acceleration vectors as a point travels around a parametrically defined curve.
Activities for the Classroom
PolarPatterns.nb PolarPatternsNew.nb	These notebooks allow students to explore the graphs of basic polar equations. They are quite similar, varying only in the amount of Mathematica assumed. The "New" version is for new users with no previous experience with the software. (Note: Neither version assumes very much!)
Sequences.nb	This allows students to look at values of sequences and then plots their values to help see patterns, convergence, and divergence. Some examples are given, and then students are asked to enter their own examples and explore on their own. (This requires very, very little knowledge of Mathematica.)
PowerDerivs.nb	Use the definition of a derivative while Mathematica does the algebra to explore the power rule for differentiating functions.
Derivb^x.nb Derivb^x.pdf	A notebook to help make sense of the derivative of exponential functions of the form y = b^x and a pdf document to complement the file. (Give students a place to write what they've just done on the computer!)
Trig(kx).nb Trig(kx).pdf	A notebook and complementary pdf file to see the effects of k in the derivatives of y = sin(kx) and y = cos(kx). This is a small beginning to the chain rule and makes students review periods and amplitudes. (This assumes knowledge of the derivatives of the Sine and Cosine functions.)
x^ksin(x^(-1)).nb	A notebook to help students look at the continuity and differentiability of functions of the form f(x) = x^ksin(1/x) at the point x = 0. This expects some basic knowledge of Mathematica* and asks students to type some complete commands by themselves.