Calculus on the Web

A Tour of the Calculus on the Web Facilities

Good evening! If this is your first time around, please take some time to read through and explore the possibilities. The local time is 10:00-- but we (almost) never close.

COW users
In this overview, you can take a look at what the COW does and how to work with it. Here are some things you can find out about: COW is an internet utility for learning and practicing calculus. It was designed at Temple by two members of the Temple University Mathematics Department, Gerardo Mendoza and Dan Reich.

The principal purpose of COW is to provide you, the student or interested user, with the opportunity to learn and practice problems in calculus (and in the future other topics in mathematics) in a friendly environment via the internet. The most important feature of the COW is that you get to know whether your answer is correct almost immediately. It is as if you had a tutor looking over your shoulder and helping you along as you work. This will be true no matter where you are or what computer you use, as long as it is connected to the internet and has a web browser.

The student component of COW (called the Manager) generates calculus examples and exercises in "modules" for studying, tutoring and practice. A number of the modules allow you to experiment by letting you change values or parameters in a function or graph and then see the effect. These modules are called "hands on" modules, and are marked with an asterisk. The component of the COW accessible by instructors (called the Reporter) handles assignment and automatic grading of homework, reporting on student work and class management.

Getting Around the COW Library

To begin a COW session, open your browser and type in the COW URL.
You will see the COW Home Page. It has a number of buttons, and some input boxes for logging in.

The COW library is organized into books, chapters and sections, with "modules" covering topics generally found in the corresponding part of a calculus text. For example, Calculus Book I contains the material normally covered in a first semester calculus course. There are also some sample modules and explanatory pages you can see by clicking on a button on the left side of this Overview page. To navigate through the cow library to a chapter or a section, to display a problem, submit an answer or to take an action of any sort, click on a button. The buttons are generally identified by the actions they control.

  • As a general rule, use the buttons provided by the COW to navigate around, not the buttons of your browser; otherwise the COW may lose track of what you were doing.
During navigation, you can see the contents of a book, a chapter or a section by clicking on the Index button.

Working with the COW

The COW system is a collection of interactive calculus modules. Each module provides the opportunity to learn and practice an individual technique or idea, or to experiment and study the variation of a particular structure. Algebra, graphics and numerical calculation are all part of the COW's repertoire.

For example, in a typical exercise module, a problem of a particular type is posed. An explanation is available, and a place to type in your answer after you have solved it in the usual way, with pencil, paper and calculator. When you submit your answer it is checked by the COW to see if it is completely, or in some cases partially, correct.

  • You must click on 'Check your answer' to make the COW aware that you have entered an answer.
After a moment of reflection, the COW will respond with a message telling you what was right or wrong about your answer, and giving you another chance if you got it wrong. In many cases, graphics are available when you submit the correct answer; in others, appropriate graphics are part of the posing of the problem.

The general philosophy of the COW system is that you have many opportunities to try a problem. If you get a problem wrong, you will always have a chance to try again. The COW rule is this:

  • You can get a problem wrong many times, but right only once!
Within a module, the problems are color-coded according to difficulty level: blue for easy ones, purple for slightly harder ones and red for the most difficult ones. In some of the modules the first few problems are ungraded. Ungraded problems are coded in black; right answers on these cannot count towards a homework grade.

Login, Recording and Grading

The COW is freely available for anyone to use, but only registered students can log in for a session in which their work will be recorded and graded. COW has the built-in ability to keep track of the user's work and calculate a sort of homework grade. This may be used by an instructor to evaluate COW homework. If COW work is a required part of a calculus course, enrolled students have to make sure this recording is turned on. If you are an enrolled student, you will have a personal COW password; recording is turned on by entering your last name and password at the bottom of the COW Home Page.

If you are logged in for a recorded session, a reminder in red will show at the top left of each screen during the session. Visitors may use the COW facility but may not have their work recorded and graded. The reminder looks like this:

This session is not being recorded
This session is being recorded for ...(your name)
The first message means that the session is not recorded at all under your name (we can't since we don't know it); if you get the second message, you gave your name and a valid password and your successes in solving the problems are being recorded.

To turn off recording when you are through working with the COW, exit the browser to terminate your work session.


Students enrolled in a class using COW may view their homework assignments by clicking on the Homework button. This button appears (during recorded sessions only) whenever you open a book (for example, by clicking on the Calculus I Book button) or when you navigate further down to a chapter, section or module. To see the content of some assignments, select the ones you want to see and click on View the assignment To work on this homework, you can simply make note of the modules involved, because once you open a module, all the homework assigned from this module will be displayed. Use the Go to button to choose a problem to work on.

After you enter the Homework screen, grade reports on your homework assignments are available via the Score the Assignment button.

Each homework assignment has a due date. The work done on an assignment must be completed by the end of the day it is due (midnight in the Eastern time zone). When an assignment is scored by the COW and reported to an instructor, only work done on or before the due date will be counted. Instructors can accomodate to individual students needing additional time to work on a particular assignment via the special due date function.

Typing Formulas

When you work with the COW, you will make your calculations by hand as usual, but you will be entering your answers into the computer. There are certain simple rules you must follow when typing in numbers or formulas. For example, how do you type in an exponent, such as "x squared" or "square root of 3"? The answers:

  • For "x squared" type x^2 ... the ^ indicates exponents.
  • For "square root of 3" type sqrt(3) or 3^(1/2).
Answers to questions like these can be found by clicking on the buttons on the left side of this Overview page; there are some help pages on typing formulas and a chance to practice, and there are some easy sample modules to introduce you to the COW's style.

Click on Typing Help for a little more detail and help.

The Reporter

Instructors in classes registered with the COW have access to the Reporter, a convenient web utility for assigning homework to a class, and generating reports on their work. The Reporter's processes are described in the Instructor Manual, accessible after logging in to the Reporter. The procedure is intuitive and requires no programming or special language. COW-registered instructors just fill in boxes and click on buttons.

Class Lists

Once a class list has been installed in electronic form in the COW system, its enrolled students will be registered and the instructor will be recognized. Classlists may be entered by instructors into the COW, and they can add and remove students individually from their classlist.

Assignments and Reports

Beyond classlist management, the Reporter has two main functions:

  • Creating and assigning COW homework for a class
  • Reporting scores on the homework or other COW work
When an instructor logs in to the Reporter, a list of the courses under his or her supervision is displayed (often just one course) in the left hand column of a table. The second column contains the list of existing assignments for each course. The third column contains a number of buttons controlling the various actions of the Reporter.

Homework Design

Instructors can create their own homework assignments and assign them to their class. To create an assignment for a given class, an instructor chooses a name and due date for the assignment, and then navigates to the appropriate section of a special index. This index lists next to each module all the problems of the module with levels of difficulty indicated. The instructor then selects problems and saves the assignment. It is automatically published to the students in that class.

There are built in procedures for editing, revising or removing an assignment, or for changing the name or due date. These procedures are quite straight- forward; the hard part is deciding which modules and problems to assign.

Special Due Dates

The Reporter looks at the due date for an assignment when scoring it and reporting on it, and will ignore work done after that date. Occasionally a student has a special reason to need an extension of time to complete an assignment, for illness or other personal matters. Using the Special due date button on the reporter main page, an instructor can change the due date for that student only.


This part of the Reporter utility produces reports on the students' COW work. These reports can be viewed via a browser or e-mailed to the instructor. There are two types of reports currently available:

  • Reports on a COW assignment or on a set of assignments
  • Reports on each student's total COW work up to that point
In the first case, instructors can choose between a simple format which reports only correctly done problems (at most once each) and a fuller format which keeps track of unsuccessful work as well. A report on total COW work will automatically be in the full report form.

One convenient feature of the reporting utility is that reports can be viewed and printed via a browser, or they can be e-mailed automatically to the instructor. An e-mailed report comes in a form which can be fed to a spreadsheet program on the instructor's local computer, so that averages and other analysis can easily be handled.