Undergraduate Course
Proposal
- Course Identification
PHYSICS 345: Symbolic Computational Methods in
Physics
Credit Hours: 3 s.h.
- Catalog Description
Symbolic computational methods involving procedural,
functional, rule-based programming and pattern matching
using the graphical and numerical capabilities of
Mathematica or other integrated mathematical software
systems, with applications to a broad range of
computationally challenging problems in physics. Prereq:
PHYS 233; Coreq: PHYS 311 and MATH 365. Offered in fall
of odd years.
- Rationale
The purpose of the course is to broaden the expertise of
the students in solving physics problems.Mathematical 1,2
is a powerful mathematical software system for students
and researchers who need an effective tool for
mathematical, analysis. Tools such as Mathematica, Maple,
Macsyma and Reduce have initiated a revolutionary way
science is taught and performed.3,4 It is a tool to
visualize and display physics concepts and to, generate
numerical and graphical solutions to physics problems. As
such, the course can serve as an appropriate supplement
for the other advanced physics courses.
- Objectives
- Students will acquire a proficiency in an
integrated mathematical software system, which
will enable them to use it fluently in their
other physics courses at the advanced
undergraduate leveland as a tool in their
research careers.
- Students will learn symbolic capabilities that
relieve them from the tediousness and errors of
lengthy and involved calculations.
- Students will learn numerical techniques that
broaden their problem-solving skills in physics.
- Students will utilize the graphical capability of
a chosen integrated mathematical. software
system, to develop their intuitions and
visualization skills in solving problems in
physics.
- Outline of Course Content
- Symbolic Computations
- Algebraic simplifications
- Polynomial factoring
- Symbolic integration
- Symbolic differentiation
- Solving system of algebraic equations
- Solving system of differential equations
- Fourier series and transforms
- Laplace transforms
- List processing
- Handling higher mathematical functions [elliptic,
Bessel, Legendre, Hermite, etc.]
- Power series
- Graphics
- Function and data plots
- 2D, 3D, and density plots
- Animated graphics
- Programming
- Procedural programming
- Functional programming
- Rule-based programming
- Pattern matching
- Numerical Computations
- Function fitting
- Integration
- Root finding
- Differential equation
- Euler's Method
- Runge-Kutta Techniques
- Applications
- Mechanics:
- FallingBodies
- ProjectileMotion
- The Pendulum
- Keplerian Orbits
- Electricity and Magnetism:
- Electric Field Lines and
Equipotentials
- Laplace's Equation
- Charged Particle in Crossed
Electric and Magnetic Fields
- Quantum Physics:
- Black Body Radiation
- Wave Packets
- Particle In a One-dimensional Box
- The Hydrogen Atom
- Criteria for Evaluating Student Performance
Student grades will be based on hands-on
performance in the lab, written and hands-on exams, and a
project using the mathematical software system (for
example, Mathematica) in some area of physics. The
project will be in the form of a "package" (equivalent
of a subroutine) in which thestudents are expected to
demonstrate their acquired skills in solving a certain
class of problems. The students will be required to
submit a printed copy of the lab exercises that they have
completed for each session.
- Reading Materials
The current textbook for the course is "A
Physicist's Guide to Mathematica" by Patrick
Tam,Academic Press, 1997.
The students will refer to their textbooks in Mechanics (PHYS
311), Modern Physics (PHYS 233),and Physics I and II with
Calculus (PHYS 231-232) for the details of physical
principles.5-10
- General Education Credit
This course may not be taken for general
education credit.
- Resources
No additional faculty or new equipment will be
needed to teach the course. The course will be taught in
the Roddy Computer Lab where Mathematica is licensed for
15 computers. Furthermore, there resources of Ganser
Library are sufficient to support the course.
- Bibliography
- S. Wolfram. The Mathematica Book,
Third Edition. Wolfram Media, Champaign, IL,1996.
- Wolfram Research. Mathematica 3.0
Standard Add-on Packages. Wolfram
Research,Champaign IL, 1996.
- D. Cook, R. Dubisch, G. Sowell, P. Tam, and D.
Donnelly. A Comparison of SeveralSymbol-Manipulating
Programs: Part I. Computers in Physics,
6(4):411-419, 1992.
- D. Cook, R. Dubisch, G. Sowell, P. Tam, and D.
Donnelly. A Comparison of SeveralSymbol-Manipulating
Programs: Part II. Computers in Physics, 6(5):530-540,
1992.
- J. B. Marion and S. T. Thornton. Classical
Dynamics of Particles and Systems,
Fourth Edition.Saunders College Publishing, Fort
Worth, TX, 1995.
- K. R. Symon. Mechanics, Third
Edition. Addison-Wesley, Reading, MA, 1971.
- R. Resnick, D. Halliday, and K S. Krane. Physics,
Fourth Edition. John Wiley and Sons,
NewYork, 1992.
- P. M. Fishbane, S. Gasiorowicz, and S. T.
Thornton. Physics for Scientists and
Engineers. Prentice-Hall, Englewood
Cliffs, NJ, 1993.
- S. Gasiorowicz. Quantum Physics,
Second Edition. John Wiley and Sons, New York,1995.
- R. Serway, C. Moses, and C. Moyer. Modern
Physics, Saunders College Publishing,New
York, 1997.