Physics 305: Computational Physics II

    Lectures:     Tu 3:30-4:50, F 1:30-2:50, Disque 704
                  zoom: https://drexel.zoom.us/my/slm23
    Office hour:  F 3:00-4:00, or by appointment
    Office:       Disque 815
    Phone:        (215) 895-2709
    e-mail:       slm23 (at) 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 the Contemporary Physics (PHYS 113, 114, 115) or the Fundamentals of Physics (PHYS 101, 102, 201) sequences. Other prerequisites are MATH 210 (Ordinary Differential Equations) and PHYS 324 (Topics in Mathematical Physics), or their equivalents. It will be assumed that the student is familiar with the Python programming language; the course will be conducted in Python. Familiarity with a more efficient lower-level language, such as C or C++, may be helpful for some applications. Students will be introduced to basic scientific programming techniques and problem-solving strategies using examples and case studies drawn from a variety of sources. Case studies will include the solution of systems of simple differential equations, investigation of the properties of chaotic systems, few-body systems in astrophysics and/or molecular dynamics, and the time-independent Schrodinger equation.

• Course syllabus

• Course outline

  1. Programming review
  2. Introductory exercises
  3. Numerical integration of ordinary differential equations
  4. Building a simple N-body code
  5. Some N-body applications
  6. Variable time steps
  7. Boundary-value problems: shooting
  8. Boundary-value problems: matrix methods

• Text

  There is no assigned text for this course. The course web site and links therein will be the primary source. Details on much of the computational material can be found in the text Numerical Recipes in C, by W. Press, S. Teukolsky, W. Vetterling, and B. Flannery (1992, Cambridge University Press). Online versions are available at http://numerical.recipes/book/book.html. The online chapters come with ``nags'' that interrupt guest access, but you can purchase a subscription, and I may place relevant excerpts on Learn.

• Topics

  • Review of Python, numpy, and matplotlib

  • Numerical differentiation and integration

  • Overview of ODEs
    • reduction to standard form
    • initial-value problems
    • boundary-value problems

  • Integration algorithms for initial-value problems
    • Euler method
    • explicit and implicit methods
    • Midpoint method
    • Runge-Kutta-4
    • applications
    • refinements
    • predictor-corrector schemes
    • the Leapfrog integrator
    • other approaches
      • more on predictor-corrector schemes
      • symplectic methods

  • Application: N-body dynamics in astrophysics and molecular dynamics
    • direct-summation techniques
    • treecodes
    • the few-body problem

  • Algorithms for boundary-value problems
    • solving algebraic equations
    • shooting
    • relaxation

  • Application: the one-dimensional Schrödinger equation

• Evaluation

  Grading will be based on roughly 6-7 homeworks. There will be no mid-term and no formal final examination. See the course syllabus for more information on homework format and grading rubric.

• Homeworks

  1. Homework #1   (solutions)

  2. Homework #2   (solutions)

  3. Homework #3   (solutions)

  4. Homework #4   (solutions)

  5. Homework #5   (solutions)

  6. Homework #6