PHYS 305: Computational Physics II

    Lectures:     Tu 12:00-1:00, Th 11:00-1:00, Disque 704
    Office:       Disque 610
    Phone:        (215) 895-2723
    Fax:          (215) 895-5934
    e-mail:       steve (at) kepler.physics.drexel.edu

Course Overview

This is the second in a series of hands-on ``computational labs'' designed to complement the traditional ``lecture/lab/recitation'' Physics instructional sequence. It is intended to be taken after PHYS 211 (Physics III) and PHYS 323 (Topics in Mathematical Physics), or their equivalents, and after MCS 210 (Ordinary Differential Equations). Students will be introduced to basic scientific programming techniques and problem-solving strategies using examples and case studies drawn from the material presented in Topics in Math. Phys. and/or ODEs. Case studies will involve the solution of systems of differential equations and investigation of the properties of chaotic systems (see course outline).

Text

There is no set text for this course. Much of the computational material will be drawn from the text Numerical Recipes in C, by W. Press, S. Teukolsky, W. Vetterling, and B. Flannery (1992, Cambridge University Press). Some material will also be distributed via the World-Wide Web. Hardcopy of selected reading may also be provided.

Topics

• Review of UNIX and X-windows
• Review of basic C programming
• Programming exercises
  
  
• Numerical integration of ordinary differential equations
  • overview of ODEs
  • integration algorithms for initial-value problems
    • a simple predictor-corrector scheme
    • the Leapfrog integrator
    • Euler method
    • Midpoint method
    • Runge-Kutta-4
    • applications
    • refinements
    • other approaches
      • more on predictor-corrector schemes
      • symplectic methods
  • applications
  
  
• Nonlinear systems and chaos
  • damped and driven harmonic motion
  • time sequences, phase portraits, and Poincare sections
  • periodic, quasiperiodic, and chaotic motion
  • self-similar structure
  • attractors and basins of attraction
  
  
• Fourier analysis of time series
• Visualization of data (if time)

Evaluation

Grading will be based on homeworks (80%) and a final project (20%). There will be no mid-term and no formal final examination.

Course outline