(Wolfram Research) Mathematica Tutorial.pdf

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CH13.NB
iii
TABLE OF CONTENTS
INFORMATION FOR INSTRUCTORS 1
1. INFORMATION FOR INSTRUCTORS
Many of the exercise sets in Thomas’ Calculus, Tenth Edition and Thomas’ Calculus, Early Transcendentals, Tenth Edition
contain Computer Algebra System (CAS) exercises, grouped in special sections labeled “Computer Explorations”, which can be
solved using Mathematica . In addition to the CAS exercises, the Thomas’ Calculus CD-ROM and Web Site contain a collection
of 38 Mathematica modules designed to help students develop a geometric intuition and deeper understanding and appreciation
of calculus concepts, methodologies, and applications. CD/Web site icons mark the locations in the text where material related
to these modules is covered.
If you plan on using (or are considering using) some of the CAS exercises or Mathematica modules associated with Thomas’
Calculus , then first spend a few minutes reading through the following information containing general advice and tips for
successfully integrating Mathematica into your course.
A. GETTING STARTED
Determine the Computing Needs of Your Students
First, you need to determine where students will complete their Mathematica assignments. If you plan on having students
complete their work on campus, then make sure that Mathematica is installed and available in the lab where students will be
working.
For those of you who need to purchase Mathematica for a campus computer lab, consider an educational site license, which will
allow your school to install Mathematica on several machines at a discounted price. Currently, Mathematica runs on most major
platforms and operating systems. For more information and technical requirements for the various platforms, visit
www.wolfram.com/products/mathematica/platforms/ . For more information on the purchasing an academic site license, go to
If Mathematica is not available on campus, then you will need to determine if it is feasible for students to purchase their own
copies of Mathematica . The student version is called Mathematica for Students and it is available at greatly reduced price (about
90% off the professional version price). Full-time students and in some cases, part-time students are eligible to purchase the
student version. Although it is available online, you may want your campus bookstore to have copies of Mathematica for
Students available for purchase. For more information about Mathematica for Students , go to
www.wolfram.com/products/student/mathforstudents/ . This site includes information on eligibility requirements for purchasing
Mathematica for Students along with information about the similarities and differences between the student version and
professional version of Mathematica .
Familiarize Yourself With the Student Computing Environment
If your students will be working with Mathematica on campus, then you will need to spend some time familiarizing yourself
with the computer lab. Be sure you determine how students log onto a computer, start the Mathematica program, quit a
Mathematica session and log out of a computer when a Mathematica session is completed. Also find out where students will
save their completed electronic files and when the computer lab will be open for student use. Keep track of all this information
and pass it on to your students.
Install Mathematica Modules and CAS Exercise Examples
Although students can access all of the Mathematica Modules on the CD/Web site, be sure you also make these files available in
an electronic folder that students can access in the computer lab. In addition, the electronic files for the CAS Computer Exercise
examples contained in this manual should also be placed in an electronic folder that students can access. These files can only be
downloaded from the Web site, not the CD-ROM. By making this material available in the lab, students will be able to download
any files they need, even if they forget to bring their CD into the lab or if they do not have internet access.
2 INFORMATION FOR INSTRUCTORS
B. PLANNING YOUR COURSE
Student Background
It will very helpful to collect some academic information about your students and to determine if they have had previous
experience working with computers. Knowing a little bit of academic information about your students may help you pick
appropriate Mathematica modules and CAS exercises to assign to your class. If you plan on having students work in pairs or
groups on computer exercises, then you may want to group together students who are less experienced at working with
computers with students who have more computer experience. If students will be doing their work in a computer lab and if there
are lab assistants working in the lab, you will probably want to provide the lab assistants with some basic information on starting
and running Mathematica .
Integrating Computer Exercises into your Syllabus
If assigning CAS exercises and/or Mathematica modules is a new experience for you, then I would recommend making the
computer exercises worth a relatively small percentage of the total points comprising the course grade. Be very selective in
which computer exercises or modules you assign and be sensitive about the amount of time it will take for students to complete
the assigned computer labs and exercises.
Familiarize Yourself with the CAS Exercises and the Mathematica Modules
Spend some time working through some of the CAS exercises and the Mathematica modules before the semester begins. By
doing this, you will get a better feel about which Mathematica modules and exercises are most appropriate for your students. If
you are new to the Mathematica computing environment, I highly recommend completing the first Mathematica module, An
Overview of Mathematica , found on the Web site and/or CD-ROM. This module will introduce you to some of the basic features
and commands of Mathematica . In addition, read through the CAS Exercise Examples contained in this computer manual and
try some of the corresponding exercises in the text to become more comfortable with the Mathematica computing environment.
C. ASSIGNING MATHEMATICA MODULES AND CAS EXERCISES
Do the Exercise Before You Assign Them
Before assigning a CAS exercise or a Mathematica module, complete the problem or module yourself. By working through the
exercise or module, you can determine if any additional instructions or hints are appropriate to pass on to your students. Another
reason for completing the work first is to make sure you are ready to answer any questions your students might have about the
assigned computer exercises. It will give you the opportunity to evaluate the length and the level of difficulty of the computer
assignment. Sometimes a given CAS exercise or module may look straightforward and easy to complete, but when you try to
solve the problem yourself, you might discover it takes more time to complete than you previously estimated.
Discuss Mathematica Assignments in Class
When you are ready to assign a CAS exercise or Mathematica module, you may want to give a brief overview of the assigned
work in class. Discuss the relevance of the assignment to the course topics you are concurrently covering in class. Neglecting to
discuss computer assignments during class may give your students the misconceived idea that the computer assignment is just
“busy work” with no real importance to the lecture material and/or written homework assignments.
Assign Only Portions of Certain Modules
It is not necessary to assign an entire module. You might find it appropriate to assign only portions of some of the modules
contained on the CD/Web site. For example, in the module Take it to the Limit , the first part of the module only covers Section
1.1 in the text while the remaining parts of the module deal with Section 1.2. Therefore, you might elect to assign only the first
part of the module to your students while you are concurrently covering Section 1.1 in the text. You may then decide to assign
the remaining parts of the module after covering Section 1.2. There may also be times when you decide to delete parts of a given
module to shorten the completion time for students. The key is to customize each module to fit the particular needs of your
course.
INFORMATION FOR INSTRUCTORS 3
Determine if Group Work is Allowed
Determine whether you want students to complete the computer assignments individually or in pairs or groups. As mentioned
earlier, one advantage of allowing or encouraging group work is that you can pair up students with weak computer backgrounds
with more computer literate students in order to help the less computer literate students adjust to the computer environment. A
disadvantage of group work is the danger of having one or two students doing all the work for the rest of the group. Whatever
you decide to do, be sure you clearly explain to students whether or not you want them to work together or individually in the
computer lab.
Determine the Acceptable Form for Completed Assignments
Be clear on how you would like students to turn in their work. If you assign one of the modules, you will probably not want
them to turn in a hard copy of every page of the completed module. Rather have them to print out a portion of the module. For
example, if the module concludes with a couple of You Try It exercises for students to complete, then you might have your
students only print the last portion of the assignment. Another possibility is have your students turn in their work electronically
on a floppy disk or to turn it in as an e-mail attachment. If you decide to have your students turn in their work electronically, be
sure to give them clear instructions about the name they should give to their file. For example, if you assign the module entitled
Take it to the Limit , then a good file name might be something like smith_lim indicating the last name of the student (Smith) and
a key descriptor of the assignment (lim for limits).
The Following Section Entitled Information for Students is Also For You!
Although the information in the following section is written for students, you should also read the next section to learn more
about the Mathematica computing environment. If you are already familiar with Mathematica , then you might want to quickly
skim through the material. However, if you are a new Mathematica user, then you may want to read the contents of the following
section very carefully.
4 INFORMATION FOR STUDENTS
2. INFORMATION FOR STUDENTS
The Mathematica modules and the CAS Exercise Examples contained on the CD/Web site were written in files called
Mathematica notebooks . Information can be entered into a notebook from the keyboard or from special files called palettes . The
purpose of this section is to discuss notebooks and palettes in more detail and to show how Mathematica commands are executed
in a notebook.
A. MATHEMATICA NOTEBOOKS
Cells
A Mathematica notebook is a file organized into a sequence of cells . Each cell contains a specific type of information that has
either been entered by the user or has been created as the result of the execution of a Mathematica command. Associated with
each cell is a cell bracket in the right margin (see Figure 1) .
Examples of Cell Brackets
Figure 1: Example of a Mathematica Notebook
There are a variety of cell types such as title and graphics cells. Perhaps the three most common types of cells, as shown in
Figure 2, are input cells, output cells and text cells. Input cells contain executable Mathematica commands. The right bracket of
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