# Calculus Laboratory Information and Materials

*On this page:*

- Calculus Laboratory Materials
- Software
- Rooms and Equipment
- Why do we have a Calculus Laboratory?
- Trivia

## Calculus Laboratory Materials

You can download a single notebook by right-clicking on it, or you can download an entire course of notebooks by clicking on its header. It is best to download an entire course if working at home, as each folder contains the stylesheet which makes the notebooks look nice.

In order to read these notebooks you must have either Mathematica or CDFPlayer. CDFPlayer is like Adobe Reader except it allows you to read Mathematics notebooks.

In order to **use** these notebooks you must have both Mathematica and calcE, both of which are free to Wright State students, faculty, and staff.

Please drop me a note if you have problems (or even if you don't!).

#### Calculus I

- Calculus I (ZIP)
- 01 Graphs and Mathematica (NB)
- 02 Functions and Graphs (NB)
- 03 Graphs and Calculus (NB)
- 04 Tangent Lines (NB)
- 05 Rates of Change (NB)
- 06 Derivatives and Graphs (NB)
- 10 The Derivative (NB)
- 11 Limits and Derivatives (NB)
- 12 Limits and Infinity (NB)
- 13 Polynomial Functions (NB)
- 14 Transcendental Functions (NB)
- 15 Algebra and Derivatives (NB)
- 16 The Chain Rule (NB)
- 20 Derivatives and Rates (NB)
- 21 Linear Approximation (NB)
- 24 Newton's Method (NB)
- 25 Optimization (NB)
- 27 Indeterminate Forms (NB)
- 28 Antiderivatives (NB)
- 29 Projects I (NB)
- 31 Area (NB)
- 32 Area and Functions (NB)
- 33 Riemann Sums (NB)
- 34 Areas and Limits (NB)
- 35 Substitution (NB)

#### Calculus II

- Calculus II (ZIP)
- 36 Integration by Parts (NB)
- 37 Partial Fractions (NB)
- 38 Trigonometric Integrals (NB)
- 39 Numerical Integration (NB)
- 40 Improper Integrals (NB)
- 41 Areas in the Plane (NB)
- 42 Volumes of Revolution (NB)
- 43 Arc Length (NB)
- 45 Differential Equations (NB)
- 49 Projects II (NB)
- 51 Vectors (NB)
- 52 Dot Products (NB)
- 53 Parametric Equations (NB)
- 61 Cross Products (NB)
- 67 Bézier Curves (NB)
- 70 Sequences and Limits (NB)
- 71 Numerical Series (NB)
- 72 Convergence (NB)
- 73 Taylor Polynomials (NB)
- 74 Taylor Series (NB)
- 75 Euler's Formula (NB)
- 76 Fourier Series (NB)

### Using Calculus Laboratory materials in Wright State computer labs and classrooms

Here are the particulars about using Calculus Laboratory materials in Wright State computer labs and classrooms.

- Mathematica with calcE is available in most or all CaTS Windows labs and in computer-equipped classrooms.
- Mathematica with calcE may not available in computer labs in Russ, but it's worth trying.
- Working in 270 MM (Mac/Windows) or 170 MM (Windows): Working in these labs is straightforward as the materials are available from the desktop, in the "Math Shared" folder.
- Working in other Wright State computer labs: When working in other labs, any Calculus Laboratory materials you wish to use must first be downloaded to the desktop from the lists above.
- Mathematica files (called "notebooks") are actually plain text files and work on any operating system—Mac, Windows, or Linux.

### Using Calculus Laboratory materials anywhere other than in Wright State computer labs, in particular at home.

Here are the details about using Calculus Laboratory materials anywhere other than in Wright State computer labs, in particular at home.

To work outside the Wright State computer labs, you will need the following:

- A computer. Mathematica is not (yet) available for tablets and smartphones.
- Mathematica software. This is available free to Wright State students by the terms of our site license.
- The calcE package is free to Wright State students, faculty, and staff.
- The Calculus Laboratory materials, which are in the format of Mathematica notebooks (files). They are available above.

Once Mathematica and calcE have been installed, you should be able to open the notebooks and work with them just as in a laboratory session.

Mathematica files (called "notebooks") are actually plain text files and work on any operating system—Mac, Windows, or Linux.

Working at home is not intended to replace the laboratory session, but rather to give you a chance to finish work begun in the laboratory. Check with your instructor concerning attendance policy —some instructors may require laboratory attendance.

## Software

### Mathematica Software

Mathematica is available FREE to all Wright State University students!

View instructions on how to set up a Wolfram account and download the program. (This is the only way to get it—you cannot copy it from another student.)

Faculty and Staff can also get Mathematica.

**Mathematica Help**

Send an email including (1) a description of the problem, (2) the saved notebook where the problem occurred (if applicable) and I will do my best to respond ASAP. Please note this only applies to problems using Mathematica. For issues concerning downloading or installing Mathematica, you need to contact CaTS.

### calcE

calcE, an add-on package for Mathematica, is necessary to use the Wright State Calculus materials for Mathematica. It is also available FREE.

**calcE** is an extension package for Mathematica which customizes it for use in mathematics instruction, in particular the teaching of calculus. The name is a contraction of "Calculus Enhanced". But the utility of **calcE** goes well beyond this particular use. The primary feature of **calcE** is improved two- and three-dimensional graphics through the **PlotE** and **Plot3DE** commands, which are useful in nearly any application where graphics are needed.

The notebook calcEPromo.nb illustrates the basic features of **calcE**. In order to view this notebook you must either have Mathematica software or the free CDF Player which allows you to read Mathematica notebooks. When you have one of these, download calcEPromo (NB) to your desktop by right-clicking on that link, then open the notebook.

Although there is no complete documentation for the features of **calcE**, its features are illustrated throughout the series of notebooks in the Calculus Laboratory Project, which can be downloaded above.

#### Download **calcE**

The following link will download the file calcE (ZIP). When expanded, it will produce a folder named calcE, containing the following files: calcE.m, init.m, Plot3DE.m, readme.txt, and TeachE.m. Because the .zip file was created on a Macintosh, extraneous files may result when expanding it in other operating systems. Just delete any extra files.

Installation is manual. In order for **calcE** to be available to Mathematica, the entire folder must be copied to an appropriate directory, which will be titled "Applications" and somehow connected to Mathematica. Here are some suggestions.

**Windows**

\Program Files\Wolfram Research\Mathematica\10.x\AddOns\Applications\

or similar directory

**Macintosh**

/Library/Mathematica/Applications

or ~/Library/Mathematica/Applications (the tilde refers to your user directory)

or similar directory

Once **calcE** has been installed in an appropriate directory, it can be loaded into Mathematica by executing either of the following commands, in the first of which the final character is a "backquote", found to the left of "1" on a standard keyboard. A backquote is also used in the second command. If you see a copyright notice, then **calcE** has loaded properly.

**<<calcE`**

**Needs["calcE`"]**

**IMPORTANT**: By downloading this file, you acknowledge that **calcE** is a copyrighted product, and that your rights are limited to installation on any computer that you personally own or manage. You do NOT have the right to redistribute **calcE** or any portion of its code in any way or by any means, whether or not there is payment involved and whether or not the code has been modified. If you know someone who is interested in calcE, please have them download it from this page as you did.

**calcE** is distributed without charge, however if you find it useful, a contribution would be greatly appreciated. The suggested amount is $25 for individuals, $10 for students and $10 per workstation for institutions. Such contributions may be made through PayPal to richard.mercer@wright.edu. No contributions are requested from anyone with an @wright.edu email address. Requests for assistance are welcome from those making such a contribution and from @wright.edu email addresses. Comments and suggestions are welcome from all!

Download calcE (ZIP) for use with Mathematica.

## Rooms and Equipment

This photo of room 270MM was taken during Spring 2009 quarter in a Calculus II class. This room currently contains 23 large-screen iMac workstations, printer, an instructor workstation with projector and Elmo, 10 standard tables, and marker boards.

Room 170MM is also used for some sections of Calculus lab. This room currently contains 26 HP Windows7 workstations, printer, an instructor workstation with projector and Elmo, and marker boards.

## Why do we have a Calculus Laboratory?

Many universities don't. Here are the reasons why we do, in order of importance:

The traditional approach to calculus is primarily algebraic, emphasizing computations done by hand with algebraic expressions. But as with nearly any mathematical topic, there are (at least!) two other approaches, geometric and numeric. These approaches are at best difficult to present without the use of technology, in many cases it is completely impractical.

For example, in the presentation of Riemann Sums (near the end of Calculus I), computers can instantly draw appropriate graphs and perform the otherwise tedious numeric computations involved, allowing instructors to concentrate on concepts, and allowing students to approach these sums as concrete objects they can manipulate. Topics throughout calculus benefit in similar ways.

When students are eventually hired in a technical position, it is unlikely that they will be expected to do any necessary mathematics on a calculator or using pencil and paper. They will almost certainly be expected to use a computer. Having a laboratory component to calculus gives them experience in doing so as part of a required course.

**A formal laboratory component provides an alternative learning environment.**During a lecture, the instructor is in charge. Students typically can participate only indirectly, by listening and attempting to follow the instructor's thoughts.

In a laboratory session, students are in charge. They have problems to solve, and must decide on their own how to approach them. When working in groups, they discuss the problems with each other. This is not only an alternative learning environment, but in many ways a superior one.

For reasons of resources and tradition, lectures are the primary instructional mode. But having a second instructional mode allows the two to reinforce each other.

**The use of technology supports the presentation of geometric and numerical approaches to mathematics****The use of technology prepares students for a technical career.**

## Trivia

**Twentieth Anniversary Calculus Lab Trivia Quiz**

In Fall 1991 a computer laboratory was used in a calculus class for the first time at Wright State. Twenty students in a section of Calculus I worked in pairs on ten computers.

- What was "special" about this section of Calculus I?
- What computers were used in the first calculus lab?
- Where was the first calculus lab located?
- What funding was obtained for the calculus lab?
- Which nearby university had a Mathematica-based calculus lab before Wright State?
- What happened on a trip to this nearby calculus lab that had a major impact on planning for WSU's lab?
- Which current member(s) of Mathematics and Statistics has(have) worked as calculus lab assistant(s)?
- On two occasions calculus labs contained computers that were neither Macintoshes nor PCs. What were they?
- Who was the only person other than myself (RM) to write notebooks that were used in the calculus lab?
- True or False:
- The calculus lab had an ethernet network before department faculty did.
- The calculus lab once had a color printer.
- The calculus lab once created and maintained its own student accounts.
- Mathematica did not support structured mathematical notation until 1996.
- There have been about 150 lab assistants, one of which became a noted Hollywood actor/actress.

Send comments and suggestions to Richard Mercer, richard.mercer@wright.edu