Physics 559, Special Topics = "Advanced Computational Physics"

This material can be found online at URL

http://spiff.rit.edu/classes/phys559/phys559.html

Course outline

Lectures

• Week 1
  • Notes on programming style
  • Pseudocode: what it is and how to use it
  • Very brief introduction to MATLAB
  • Euler's method for numerical integration
• Week 2
  • Higher-order methods, in the simple case
  • Higher-order methods, in not-so-simple cases
  • Input and output arguments in MATLAB functions
  • The fourth-order Runge-Kutta method
  • A simple look at error analysis
• Week 3
  • Moving into two (or three) dimensions
  • Using conserved quantities as checks on your simulation
  • How to cheat when simulating gravity
  • Changing the timestep in your simulation
• Week 4
  • Accuracy vs. timestep for different techniques
  • How to simulate stellar motion within a galaxy
• Week 5
  • Checking the values of input arguments
  • Numerical treatment of heat conduction
  • Derivatives and differences
  • Numerical treatment of heat conduction in 2-D
• Week 6
  • A dynamic look at heat conduction
  • A step-by-step look at numerical (in)stability
• Week 7
  • A new boundary condition: insulated end
  • One more boundary condition: radiative end
• Week 8
  • Choosing an independent project
• Week 9

Homework / Programming assignments

In order to submit your work, use the "dropbox" facility for this course at mycourses . When you submit a program, you should give it a name in the following manner: each assignment will involve writing a function with some specific name -- for example: simple_toss.m. You will use that name for all your development and testing. When you want to submit your work, please prepend to the name your initials, in lower-case letters, and an underscore character. Thus, a student with name "John Q. Public" would submit a file called

      jqp_simple_toss.m

• Week 1:
  • Pseudocode for "motion of a ball" program (due in class, Wednesday, Nov 28)
• Week 2:
  • Motion of a ball (due: Fri, Dec 7, at 5 PM)
  • Extra credit: Perfect numbers (due Friday, Dec 7, at 5 PM)
• Week 3:
  • The orbit of a satellite (due Fri, Dec 14, at 5 PM)
  • Extra credit: the tiny Earth experiment (due Fri, Dec 14, at 5 PM)
• Week 4:
  • Motion of bodies in the solar system (due Fri, Dec 21, 2012 at 5 PM)
• Week 5:
  • Steady-state temperature of a thin rod (due Fri, Jan 11, 2013 at 5 PM)
  • Extra credit: A thin rod, using linear algebra (due Wed, Jan 16, at 5 PM)
• Week 6:
  • Steady-state temperature on a thin plate (due Fri, Jan 18, 2013 at 5 PM)
• Week 7:
  • Dynamic temperature of a long, thin rod (due Fri, Jan 25, 2013 at 5 PM)
• Week 8:
  • Grilling a hamburger (due Fri, Feb 1, 2013 at 5 PM)
• Week 11:
  • The final project (due Thursday, Feb 21 at 5 PM)

Example programs

• guess.m plays a guessing game with the user
• A series of 3 very short and simple functions which illustrate the basic form of a MATLAB function.
  • gluttony.m simply prints a fixed message. ( pretty version)
  • gluttony_with_args.m illustrates the use of input arguments ( pretty version)
  • gluttony_counter.m includes a little loop ( pretty version)
• grav_example_euler1.m illustrates the dangers of using a simple algorithm to integrate the motion of objects due to gravity -- when those objects grow too close.
• cool_off.m employs Euler's method and Newton's Law of Cooling to compute the temperature of an object as a function of time. You might prefer to look at the pretty HTML version of cool_off.m instead of the MATLAB program itself.
• sieve.m shows how to define and use two functions within a single MATLAB source code file. It uses the Sieve of Eratosthenes to look for prime numbers within some specified range. The HTML version might look better in a browser.
• solar_system.m is an outline of the structure one might use for the solar system program. It is by no means complete.

For more information

• SPSP 317: Introduction to Computational Physics contains materials for my version of the introductory course in computational physics. You will find links to many programming resources there, and examples of programs in the Scilab language, which is very similar to MATLAB.
• There are books on reserve in the library which may help you with this course.
  • Numerical Methods for Engineers, by Chapra and Canale, fifth edition. A copy of the second edition of this book is on the bookshelf in the PAC.
  • Applied Numerical Methods with MATLAB for Engineers and Scientists, by Chapra.

This page maintained by Michael Richmond. Last modified Feb 2, 2012.