Computation in Undergraduate Physics:
The Lawrence Approach

Poster Mounted at the Summer Meeting
of the American Association of Physics Teachers
Sacramento, CA
3 August 2004

David M. Cook
Department of Physics
Lawrence University
Box 599
Appleton, WI 54911-5626


920-832-6721

Email: david.m.cook@lawrence.edu

Department website: http://www.lawrence.edu/dept/physics

Project website: http://www.lawrence.edu/dept/physics/ccli

Abstract

Since the mid 1980s, the Lawrence Department of Physics has been striving to embed the use of general purpose graphical, symbolic, and numeric computational tools throughout our curriculum. Developed with support from the National Science Foundation, the Keck Foundation, and Lawrence University, our approach involves introducing freshman to tools for data acquisition and analysis, offering sophomores a course that introduces them to symbolic, numerical, and visualization tools, incorporating computational approaches alongside traditional approaches to problems in many intermediate and advanced courses, and making computational resources available so that students come to see them as tools to be used routinely on their own initiative whenever that use seems appropriate. A flexible text that is microscopically customizable to reflect many different choices of hardware and software is now complete. Details about the Lawrence curricular approach and about the text are posted on the project web site at www.lawrence.edu/dept/physics/ccli.

Poster

Underlying Convictions

Students must learn to use:

Students must learn to use these tools for

Students must


Typical Physics Program

Note: ** = required for minimum physics major; boldElective = explicit use of computers

Term ITerm IITerm III
Freshman Freshman StudiesFreshman StudiesElective
**Calculus I**Calculus II**Calculus III
Elective**Intro Class Phys**Intro Mod Phys
Sophomore **Electronics**Computational Mechanics **E and M
**Linear Algebra/ODEElectiveElective
ElectiveElectiveElective
Junior **Quantum Mechanics**Advanced Lab**Physics Elective
LanguageLanguageLanguage
ElectiveElectiveElective
Senior %Elective**Physics Elective**Physics Elective
ElectiveElectiveElective
ElectiveElectiveElective

% Often independent research in physics, but not required for the major

Available Physics Electives


Curricular Components

Freshman Year:

Sophomore Year:

Junior/Senior:


Computational Mechanics

(Required of sophomores}

Note: The text for the computational components of this course (and for many other computational dimensions of the Lawrence curriculum) is published in a variety of formats. A full description of the project culminating in that text---and of the text itself will be found from links assembled wat the URL http://www.lawrence.edu/dept/physics/ccli.

Catalog Description

Introduces symbolic and numerical computation through examples drawn mainly from classical mechanics but also from classical electromagnetism and quantum mechanics. This course emphasizes computer-based approaches to graphical visualization, the solution of ordinary differential equations, the evaluation of integrals, and the finding of eigenvalues and eigenvectors. Prerequisites: Introductory Classical Physics, Differential Equations and Linear Algebra.

Weekly Schedule

Wk 01 Orientation to UNIX, including Text Editor
Kinematics and Dynamics of Translation and Rotation
Impulse/Momentum/Work/Kinetic Energy
Gravity/Electromagnetic Forces/Friction/Tension

WK 02Orientation to IDL/TGIF (basic capabilities; visualization)

WK 03Equations of Motion:
** Constant force/torque
** Force dependent only on time
** Force dependent only on position
Potential energy, SHM and equilibrium
Work and potential energy in 3D

WK 04Velocity-dependent forces
Damped and driven SHM
Resonance
Coupled Oscillations

WK 05 HOUR EXAMINATION
Orientation to LaTeX
Central forces, effective potential, orbital equation

Wk 06Planets, Satellites, Comets
MID-TERM READING PERIOD

WK 07Orientation to MAPLE
Using MAPLE to Solve ODEs
Algorithms to Solve ODEs Numerically

WK 08Using IDL to Solve ODEs Numerically fff

WK 09HOUR EXAMINATION
Symbolic Evaluation of Integrals

WK 10Algorithms to Evaluate Integrals Numerically
Using IDL to Evaluate Integrals Numerically

WK 11FINAL EXAMINATION


Computational Physics

(Junior/senior elective)

Catalog Description

Treats computational approaches to problems in physics with particular emphasis on finite difference and finite element methods for solving partial differential equations as they arise in electromagnetic theory, fluid mechanics, heat transfer, and quantum mechanics, and on techniques for graphical visualization of the solutions. Prerequisites: Computational Mechanics.

Weekly Schedule

(Note: This schedule is subject to revision. The course will be offered for the first time in the fall of 2004.

Wk 01 Review of Numerical Approach to ODEs, IDL

WK 02Analaytic/Physical Derivation of PDEs
** Wave Equation
** Diffusion Equation
** Laplace Equation
**Equatiions of Fluid Dynamics

WK 03Finite Difference Methods (FDM) for
PDEs, using IDL and FORTRAN

WK 04LSODE for Wave Equation and Diffusion Equation

WK 05 HOUR EXAMINATION
MUDPACK and Multigrad Techniques for Elliptic PDEs

Wk 06Multigrid Techniques (continued)
Introduction to Finite Element Methods (FEM)
MID-TERM READING PERIOD

WK 07FEM with IDL, FORTRAN

WK 08HOUR EXAMINATION
FEM with MARC/MENTAT

WK 09FEM with MARC/MENTAT (continued)
Start Individual Projects

WK 10Finish Projects
Oral Reports on projects
Written reports due at emd of week
NO FINAL EXAMINATION