Strengthening Computation in Upper-Level

Undergraduate Physics Programs

David M. Cook

Department of Physics, Lawrence University, Box 599, Appleton, WI 54911-5626

Voice: 920-832-6721; FAX: 920-832-6962; Email:

Text of Talk Delivered at the Summer Meeting of the American Association of Physics Teachers

University of Guelph, Guelph, Ontario

31 July 2000


For more than a decade, the Department of Physics at Lawrence University has been introducing sophomore majors to graphical, symbolic, and numerical computation, orienting them early on in physical contexts to general purpose tools for graphing scalar and vector fields, evaluating integrals, solving ODEs and PDEs, finding roots, processing experimental data, and preparing technical manuscripts. We aim throughout to develop confidence and independence in the use of these tools. With support from NSF CCLI-EMD grant DUE-9952285, the author is embarking on a two-year project whose main objectives are (1) to recast numerous locally written materials into a publication that can be easily customized for use with a variety of hardware and software and (2) to develop an effective mechanism for distribution. The grant also supports faculty workshops to be held at Lawrence University in the summers of 2001 and 2002 and modest beta testing in 2001-02.


Usually, reports at these meetings describe completed projects. I want instead to introduce a project that is just getting underway. Many of you probably know that, for a dozen years or more, we at Lawrence University have been developing the computational dimensions of our upper-level curriculum. We have built a computational laboratory that makes a wide spectrum of hardware and software available to students and, concurrently, we have developed numerous documents introducing computational tools and describing prototypical applications.

The LU Course

The starting point in our nurturing of our students' computational skills is a sophomore elective course called Computational Tools in Physics. This full-credit course is offered in three 1/3-credit segments, one in each of the three terms of our academic year. Its topics are coordinated with the sequence of required courses taken by sophomore physics majors. The first term addresses the topics

and focuses on acquainting students with the rudimentary capabilities of our Computational Physics Laboratory (CPL). In each class, students are introduced to a particular computational tool. Then, each student works several exercises, ultimately turning in written solutions prepared with LaTeX. Class sessions provide only orientation and motivation; students are expected to exhibit a fair bit of personal independence and aggressiveness in moving from the starting point provided by classes to the knowledge and skill needed to finish the assignment.

The second term is coordinated with an intermediate course in classical mechanics and focuses on symbolic and numerical approaches to ordinary differential equations. In the first half of the term, it covers

Each student completes this term by carrying out an extended (5 week) project that culminates in a written paper and a 20-minute oral presentation to the class. Topics like the three-body problem, coupled oscillators, the compound pendulum, enharmonic oscillators, and chaos have been addressed.

The third term is coordinated with an intermediate course in electricity and magnetism and focuses on symbolic and numerical integration. In the first six weeks of the term, it covers

This term also concludes with an extended (4 week) project, written paper, and 20-minute oral presentation. Topics like electric fields and potentials, magnetic fields, Fourier analysis, non-linear least squares fitting, and global positioning systems have been addressed.

The Lawrence approach to nurturing the abilities of students to use computational resources

Our approach is active; it compels students to play a personal role in their own learning; it forces students to defend their solutions in writing; it gives students practice in preparing and delivering oral presentations; it encourages students to work in groups; and, more than any other objective, it develops the students' abilities to operate on their own initiative.

Next Steps

The grant referenced in the abstract and received last February from the Educational Materials Development track of the Course, Curriculum, and Laboratory Improvement program (CCLI-EMD) of the NSF provides support for converting the experience acquired and the extensive library of instructional materials developed at Lawrence into a flexible publication as a resource for other institutions. That we don't all have the same spectrum of hardware and software, however, poses a major challenge. I believe that meeting that challenge begins by recognizing that our materials can be divided into two groups. Modules that identify physical contexts in which computational tools are useful or discuss general computational approaches are generic; modules that introduce features of an operating system or describe the commands needed to use a particular software package are hardware or software dependent. Beyond creating the modules themselves, I will over the next couple of years be working with Brooks-Cole to develop a mode of publication that will allow each individual instructor to assemble selected modules into a text that is microscopically tailored to that instructor's specific circumstances. Week-long faculty workshops and site testing beyond Lawrence will help to refine the end product and contribute to its dissemination. While not included in the basic plan, the option for individual instructors to add their own modules to the available spectrum is likely to emerge in due time. In the next few transparencies, I hope to convey some of my present conception of what the final product will look like. Here, with the broadest brush, is my present tentative table of contents:

  1. Overview of Materials
  2. Introduction to IDL or MATLAB or ...
  3. Introduction to MACSYMA or MAPLE or Mathematica or ...
  4. Introduction to Programming in FORTRAN or C
  5. Introduction to Numerical Recipes
  6. Solving ODEs
  7. Evaluating Integrals
  8. Finding Roots
  9. Solving PDEs
  10. Data Analysis/Curve Fitting
  11. Fourier Analysis and Image Processing
  12. Publishing with LaTeX or HTML or ...
Note the following: While the objective is for students to become fluent in the use of a spectrum of computational tools---and the chapters are organized by program or by computational technique involved, the focus throughout is on physical contexts.

Let us look now in a bit more detail at Chapters 2 and 7, which are representative of the two basic types of chapter. Chapter 2 represents chapters that introduce basic features of an application program, specifically a program for processing arrays of numbers and creating graphical visualizations of one-, two-, and three-dimensional data sets. Whether the chapter deals with IDL or MATLAB or some other similar computational tool, its sections are tentatively titled

The bulk of the chapters in this category will be structured as tutorials and will lean in some measure on vendor's documentation and on-line help to encourage and guide self-study.

The structure of Chapter 7 on evaluating integrals exemplifies the structure of all of the chapters on various computational techniques. Presumably, before approaching any particular section in this chapter, the student would have studied the relevant sections in earlier chapters. Tentatively, the sections in Chapter 7 are titled

The first section, whose detail we will look at in a moment, sets several physical problems, the successful addressing of which benefits from exploitation of a computational tool. The second section describes how one might use a symbolic tool in application to some of the problems set in the first section. Save for the last, the remaining sections describe suitable numerical algorithms generically and then illustrate how those algorithms can be invoked in a variety of ways. The final section lays out several exercises that students can use to hone their skills. Sections 7.1 (sample problems), 7.3 (numerical algorithms), and 7.7 (exercises) would be included in all versions of the chapter; each individual instructor would select only those other sections that are appropriate to that instructor's site.

Let us step down one further level in the envisioned structure. Here is the present list of sample problems to be laid out in the first section of Chapter 7:

They range over several subareas of physics and reveal that evaluation of integrals, perhaps as functions of one or more parameters, plays an important role in many areas of physics.

Because several aspects of computer use at a specific site are unique to that site, use of the materials I seek to create will require that, at each site, someone take responsibility for creating a local guide, to which the materials will refer. This local guide will provide information about a variety of local conventions, including

Among the supplementary materials I must create will be a template for this local guide.

Achieving Flexibility

Finally, let me speak briefly about how I think the necessary flexibility in publishing can be achieved. Beyond doing a superb job of formatting complex equations, tables, arrays, and text, the package LaTeX is able to create tables of contents and indices automatically. One of the available packages (the ifthen package), when invoked, adds a capability to include or exclude different files depending on whether a controlling Boolean variable has the value `true' or `false'. Thus, one

At the end of this set of activities, one then has the original that can be used to make however many copies are needed. It's THAT easy!!!

Brooks-Cole is committed to participating in the process of refining this essential procedure so as to be able to make a commercially feasible product. Their editors claim that they will be able to produce the desired customization economically for orders as few as ten copies.

Post Script

I began by declaring that I was going to depart from tradition and announce a project that is only now getting underway. With the exception of one three-month period, I will be devoting essentially full time to this project from now until December, 2001. The finished manuscript will be delivered to the publisher by September, 2002. I have elected to announce the project now at its inception and I intend to deliver progress reports in San Diego and Rochester, because I need your help. I welcome

Finally, let me mention that I have with me a couple of copies of the current draft---please understand DRAFT---of a couple of chapters. Though the text is not at all ready for any kind of preliminary distribution, I would be happy to let anyone interested in seeing greater detail take a look at these drafts, either after this session or at any time before these meetings end.