Undergraduate Course Proposal

  1. Course Identification
    PHYSICS 345: Symbolic Computational Methods in Physics
    Credit Hours: 3 s.h.
  2. 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.
  3. 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.
  4. Objectives
    1. 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.
    2. Students will learn symbolic capabilities that relieve them from the tediousness and errors of lengthy and involved calculations.
    3. Students will learn numerical techniques that broaden their problem-solving skills in physics.
    4. 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.
  5. Outline of Course Content
    1. Symbolic Computations
      1. Algebraic simplifications
      2. Polynomial factoring
      3. Symbolic integration
      4. Symbolic differentiation
      5. Solving system of algebraic equations
      6. Solving system of differential equations
      7. Fourier series and transforms
      8. Laplace transforms
      9. List processing
      10. Handling higher mathematical functions [elliptic, Bessel, Legendre, Hermite, etc.]
      11. Power series
    2. Graphics
      1. Function and data plots
      2. 2D, 3D, and density plots
      3. Animated graphics
    3. Programming
      1. Procedural programming
      2. Functional programming
      3. Rule-based programming
      4. Pattern matching
    4. Numerical Computations
      1. Function fitting
      2. Integration
      3. Root finding
      4. Differential equation
      5. Euler's Method
      6. Runge-Kutta Techniques
    5. Applications
      1. Mechanics:
        • FallingBodies
        • ProjectileMotion
        • The Pendulum
        • Keplerian Orbits
      2. Electricity and Magnetism:
        • Electric Field Lines and Equipotentials
        • Laplace's Equation
        • Charged Particle in Crossed Electric and Magnetic Fields
      3. Quantum Physics:
        • Black Body Radiation
        • Wave Packets
        • Particle In a One-dimensional Box
        • The Hydrogen Atom
  6. 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.
  7. 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
  8. General Education Credit
    This course may not be taken for general education credit.
  9. 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.
  10. Bibliography
    1. S. Wolfram. The Mathematica Book, Third Edition. Wolfram Media, Champaign, IL,1996.
    2. Wolfram Research. Mathematica 3.0 Standard Add-on Packages. Wolfram Research,Champaign IL, 1996.
    3. 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.
    4. 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.
    5. J. B. Marion and S. T. Thornton. Classical Dynamics of Particles and Systems, Fourth Edition.Saunders College Publishing, Fort Worth, TX, 1995.
    6. K. R. Symon. Mechanics, Third Edition. Addison-Wesley, Reading, MA, 1971.
    7. R. Resnick, D. Halliday, and K S. Krane. Physics, Fourth Edition. John Wiley and Sons, NewYork, 1992.
    8. P. M. Fishbane, S. Gasiorowicz, and S. T. Thornton. Physics for Scientists and Engineers. Prentice-Hall, Englewood Cliffs, NJ, 1993.
    9. S. Gasiorowicz. Quantum Physics, Second Edition. John Wiley and Sons, New York,1995.
    10. R. Serway, C. Moses, and C. Moyer. Modern Physics, Saunders College Publishing,New York, 1997.