THE CATHOLIC UNIVERSITY OF AMERICA PHYSICS DEPARTMENT

Course description:

Course Goals:

• This course will cover a variety of numerical methods that can be applied to solve algebraic problems and differential equations, in particular when a closed solution is not available.
• Algorithms will be adapted to solve specific problems in fields that will be decided during the first session in class. Suggested fields are:
  • multi-body systems (e.g. molecular systems, planetary systems, ...),
  • non-linear oscillations (e.g. coupled oscillators, oscillators in polarizable media, ...),
  • chaotic dynamics (self-similarity, stability of solutions, kinetic growth models, fractals, ...),
  • electrodynamics/optics (interference, diffraction, moving charges, MHD, ...),
  • thermodynamics (kinetic theory, Ising model, ...),
  • hydrodynamics (diffusion eq., turbulences, ...).
  As of 9/1/09 we decided to do some E&M applications, in particular MHD (using ODE solving techniques), and kinetic growth models (using Monte Carlo method).
• The course will be held in part as lecture, in part as seminar course: each student is required to make two presentations of her/his approach and solution of given problems.
• All problems can be worked out using Mathematica, Maple, MatLab. We finally got a campus license for Mathematica! Knowledge of a programming language (e.g. fortran, c, c++, java) will be very helpful, esp. in the context of Monte Carlo simulations.
• You are encouraged to improve your software skills by applying the discussed algorithms to some examples.

Textbooks:

• Numerical and Analytical Methods for Scientists and Engineers Using Mathematica, by D.Dubin, 2003, Wiley.
• Numerical Methods for Physics, by A.L.Garcia, 1994, Prentice Hall.
• Numerical Recipes. The Art of Scientific Computing, by W.I. Press et al, 2nd ed. 1992 or 3rd ed. 2007, Cambridge U. Press.
• Computational Physics, by N.J. Giordano and H. Nakanishi, 2nd ed. 2005, B. Cummings Press.
• Statistical and Computational Methods in Data Analysis, by S. Brandt, 3rd ed. 1999, North-Holland Publishing.
• Fundamental of Stochastic Signals, Systems and Estimation Theory, by B. Kovacevic and Z. Durovic, 2nd ed. 2008, Springer.
• Mathematica for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics, by G.Baumann, 2nd ed. 2005, Springer.
• Mathematica for Theoretical Physics: Electrodynamics, Quantum Mechanics, General Relativity, and Fractals, by G.Baumann, 2nd ed. 2005, Springer.

Expectations:

• Academic honesty: Academic honesty is expected of all CUA students. Faculty are required to initiate the imposition of sanctions when they find violations of academic honesty, such as plagiarism, improper use of a student’s own work, cheating, and fabrication.
  The following sanctions are presented in the University procedures related to Student Academic Dishonesty (from http://policies.cua.edu/academicundergrad/integrityprocedures.cfm"): “The presumed sanction for undergraduate students for academic dishonesty will be failure for the course... In the context of graduate studies, the expectations for academic honesty are greater, and therefore the presumed sanction for dishonesty is likely to be more severe, e.g., expulsion. ... In the more unusual case, mitigating circumstances may exist that would warrant a lesser sanction than the presumed sanction.”
• Assignments and research exercises have to be submitted before the due date. Any necessary delays must be announced to the instructor as promply as possible.
• Accomodations for students with disabilities: Any student who feels she/he may need an accomodation based on the impact of a disability should contact the instructor privately to discuss specific needs. Please contact Disability Support Services (at 202-319-5211, room 207 Pryzbyla Center) to coordinate reasonable accomodations for students with documented disabilities. To read about the services and policies, please visit http://disabilitysupport.cua.edu.

Homework and Exam:

• There will be homework problems assigned every week.
• Presentations will count for 40% of your grade and homework will count for 40%. The final exam, scheduled for Tuesday, December 15, will count for 20% of your grade.
• Anyone who is unable to attend the scheduled exam should arrange ahead of time for an alternate date.