Computation in undergraduate physics: The Lawrence approach

The Physics Curriculum Workshop Conference on Computers in Undergraduate Science Education sponsored by the Commission on College Physics (CCP) and held at Illinois Institute of Technology in August 1970, was among the first national gatherings of those who recognized the potential of the new technology. A CCP publication, Computer-Oriented Physics Problems, edited by J. W. Robson, and published in August 1971 emerged from that conference as an early effort to provide modules for incorporation into traditional courses.

Alhough now dated, pertinent publications include

A. M.

Bork

, (, Reading, MA, );

H.

Peckham

, (, Reading, MA, );

R.

Ehrlich

, (, Boston, ); and

J.

 

Merrill

, (, Boston, ).

See, for example,

W. M.

MacDonald

,

E. F.

Redish

, and

J. M.

Wilson

, “,”  (), – ();

P.

Laws

, “,” in , edited by

E. F.

Redish

and

J.

Risley

(, Reading, MA, ), pp. –;

M. L.

DeJong

, “,”  (), – ();

W. G.

Harter

, “,”  (), – ();

P.

Laws

, “,”  (), ();

J. M.

Wilson

, “,”  (), – ();

J. M.

Wilson

,

E. F.

Redish

, and

C. K.

McDaniel

, “,”  (), – (); and

“,”  (), – ();

J. M.

Wilson

, “,”  (), – ();

W.

Christian

and

M.

Belloni

, (, San Francisco, ) and

(, San Francisco, );

R. W.

Chabay

and

B. A.

Sherwood

, (, New York, ), 2nd ed., and

(, New York, ), 2nd ed.

See, for example, the American Institute of Physics report on the 1998–99 Bachelor’s Plus Five Study (search “Bachelor’s Plus Five” at $⟨$www.aip.org$⟩$⁠), which documents that five to eight years after graduation, about 25% of those with a physics undergraduate degree and no higher degree declare that they are employed in “software.” Surely, the 30% who declare they are employed in “science and lab” or “engineering” also use computational resources to some extent. In the same study, about 45% of the graduates rate “computer programming” as “very important,” and only about 37% rate “physics principles” and 33% rate “knowledge of physics” as “very important” job skills.

For a review of several studies and citations to the studies, see

O.

Yaşar

and

R. H.

Landau

, “,”  (), – (), which is available at $⟨$epubs.siam.org/SIREV/sirev-toc.html$⟩$⁠.

The importance of incorporating computation in the undergraduate physics curriculum is also discussed in

N.

 

Chonacky

and

D.

 

Winch

, “,”  (&5), – ().

In this listing, when two publication dates appear, the first is the date of publication of the first edition. See, for example,

W. J.

Thompson

, (, New York, );

H.

Gould

,

J.

Tobochnik

, and

W.

Christian

, (, Reading, MA, ; 2006), 3rd ed.;

M. L.

DeJong

, (, Reading, MA, );

A.

Garcia

, (, Upper Saddle River, NJ, ; 2000), 2nd ed.;

P. L.

DeVries

, (, New York, );

(CUPS), edited by

R.

Ehrlich

,

W.

MacDonald

, and

M.

Dworzecka

(, New York, )

[This project yielded nine volumes written by 29 authors for use in standard intermediate and advanced courses on Electricity and Magnetism, Astrophysics, Quantum Mechanics, Classical Mechanics, Nuclear and Particle Physics, Waves and Optics, Thermal Physics, Modern Physics, Solid State Physics.];

N.

Giordano

and

H.

Nakanishi

, (, San Francisco, ; 2005), 2nd ed.;

R. H.

Landau

and

M.

Páez

, (, New York, );

R. H.

Landau

 et al, (, Princeton, NJ, );

A.

 

Shiflet

and

G.

 

Shiflet

, (, Princeton, NJ, ).

See, for example,

P. B.

Visscher

, (, New York, );

J.

Feagin

, (, Berlin, );

R.

Greene

, (, Berlin, ; 2000), 2nd ed.;

J.

 

Hasbun

, (, Boston, ).

This project is described in detail in Ref. 3, Chonacky and Winch.

The specific citations in this paragraph identify representative activities. The author does not claim to have cited or to be aware of all contributors and apologizes to those omitted. A more comprehensive listing can be found in

R. H.

 

Landau.

“,”  (&5), – (). The September/October 2006 issue of Computing in Science and Engineering is on “Computation in Physics Courses.” It includes the results of a national survey of uses of computers in undergraduate physics, the texts of five invited papers delivered at the Syracuse meeting of the AAPT in the summer of 2006, and abstracts of the seventeen invited posters at the same meeting.

See, for example,

M.

Belloni

and

W.

Christian

, “,”  (), – ();

M.

 

Belloni

,

W.

 

Christian

, and

A. J.

 

Cox

, (, San Francisco, ).

See, for example,

D. M.

Cook

, “,”  (), – ();

D. M.

Cook

, “,”  (), – ();

K. R.

 

Roos

, “,”  (), – ().

An early course in computational physics was described by

W. J.

Thompson

in “,”  (), – (), and

an unusual approach is described by

R. H.

 

Landau

,

H.

 

Kowalik

, and

M.

 

J. Páez

in “,”  (), – (), but such courses now exist at numerous institutions. Some have been described in presentations at professional meetings (Ref. 7), but few have been described in detail in the literature. In many cases, these courses also play a role in full-blown computational majors or computational tracks (Ref. 11).

Such an approach is in place at Oregon State University and Austin Peay State University. See

R. H.

Landau

, “,”  (), – ();

R. H.

Landau

, “,”  (), – (); and

J. R.

 

Taylor

and

B. A.

 

King III

, “,”  (), – (). A survey of several such programs is incorporated in Ref. 3, O. Yaşar and R. H. Landau.

See, for example,

R. F.

Martin

,Jr. ,

G.

Skadron

, and

R. D.

Young

, “,”  (), – ();

D. M.

Cook

, “,”  (), – (); and

“,”  (), – ();

W.

Christian

, “,”  (), – ();

D. M.

Cook

, “,” in , edited by

V. N.

Alexandrov

 et al (, Berlin, ), Part 1, pp. –;

M.

 

Johnston

, “,”  (), – (); J. R. Taylor and B. A. King III, Ref. 11.

See EPAPS Document No. E-AJPIAS-76-011803 for an 82-page report titled “,” which includes detailed syllabi for the central courses, sample assignments and examinations, and a description of the text used in these courses. This document can be reached through a direct link in the online article’s HTML reference section or via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html).

For example, IDL, ITT Industries, $⟨$www.ittvis.com$⟩$ and MATLAB, The MathWorks, ⟨www.mathworks.com⟩. OCTAVE is available under a GNU General Public License, $⟨$www.octave.org$⟩$⁠.

For example, MAPLE, Waterloo Software, ⟨www.maplesoft.com⟩ and MATHEMATICA, Wolfram Research, ⟨www.wolfram.com⟩. MAXIMA, is available under a GNU General Public License, ⟨maxima.sourceforge.net⟩.

For example, KALEIDAGRAPH, Synergy Software, www.synergy.com, and/or IDL, MATLAB, and OCTAVE (Ref. 14).

For example, MULTISIM, Electronics Workbench Corporation, $⟨$www.electronicsworkbench.com$⟩$⁠; SPICE is available at nominal cost (start at $⟨$www.berkeley.edu$⟩$ and search for SPICE).

For example, LABVIEW, National Instruments Corporation, $⟨$www.NI.com/labview$⟩$⁠.

For example, LATEX is freely available for many platforms via $⟨$www.tug.org$⟩$⁠.

For example, TGIF, $⟨$bourbon.usc.edu/tgif$⟩$⁠.

D. M.

Cook

, (, Appleton, WI, );

D. M.

 

Cook

, (, Appleton, WI, ). Contact the author for detailed information.

The LabPro hardware and assorted sensors connect externally to a laboratory computer and, in conjunction with the associated software, LOGGERPRO, provide facilities for on-line data acquisition. Vernier Software and Technology, $⟨$www.vernier.com$⟩$⁠.

Spectrum Techniques, LLC, $⟨$www.spectrumtechniques.com$⟩$⁠.

NanoScience Instruments, $⟨$www.nanoscience.com$⟩$⁠.

Finite difference methods involve overlaying a grid of uniformly spaced nodes on the domain of the problem and discretizing the PDE by using finite differences to approximate the first and second partial derivatives of the solution, for example, $(∂u∕∂x)i,j≈[u(xi+1,yj)−u(xi−1,yj)]∕(2Δx)$ for the first derivative at node $(i,j)$⁠. If only the space variables are discretized, the PDE is replaced with a set of coupled ODEs to be solved for the approximate temporal behavior of the solution at each node. If the time variable is also discretized (or if there is no time variable), the PDE is replaced by a set of algebraic equations for the solution at each node.

See, for example,

G. E.

 

Forsythe

and

W. R.

 

Wasow

, (, New York, ), which is available in a Dover reprint.

The subroutine lsode (the Livermore Solver for ODEs) is a component of ODEPACK, which is a large package containing numerous FORTRAN solvers for ODEs. This package is in the public domain. See $⟨$www.netlib.org/odepack$⟩$⁠.

MUDPACK is a package containing numerous FORTRAN solvers for elliptic partial differential equations in two and three dimensions. This package is in the public domain. See $⟨$www.scd.ucar.edu/css/software/mudpack$⟩$⁠.

Finite element methods involve overlaying a network of arbitrarily positioned and not necessarily regularly spaced nodes on the domain of the problem, connecting those nodes to cover the domain with elements (lines in one dimension, triangles or quadrilaterals in two dimensions, tetrahedrons or bricks or other geometries in three dimensions), selecting an approximating function for each element, and determining the constants in those approximating functions so that (1) the difference between the approximating function and the actual solution throughout each element is minimized by one of several criteria and (2) continuity of the function and its first derivatives at the boundaries between elements is assured. The method, which replaces the PDE with a set of algebraic equations for the solution at the nodes, is more complicated than finite difference methods, but is much more easily applied to problems with irregular geometries.

For more details see, for example,

J. E.

Akin

, (, London, );

D. S.

Burnett

, (, Reading, MA, );

L. R.

 

Ram-Mohan

,

S.

 

Saigal

,

D.

 

Dossa

, and

J.

 

Shertzer

, “,”  (), – (), and references therein.

MARC/MENTAT is a pair of programs for setting up and solving partial differential equations by finite element techniques and can be leased from MSC Software, $⟨$www.mscsoftware.com$⟩$⁠. Another finite element package is FEMLAB, $⟨$ecs.rutgers.edu/eitlab$⟩$⁠, which is an add-on to MATLAB.