General Information:

• Course description
• Course outline
• Text and books on reserve in Physics Library
• Grade
• Computing

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Course description:

This course is part of the Applied Science core sequence in math and computational methods. Building on the applied mathematics topics introduced in the first part of this course in the Fall, we will here take a more ``applied'' approach and focus more on computations, exposing computational and applied mathematical techniques through examples in physical sciences. We will cover general computational methods, such as Monte Carlo, molecular dynamics, cellular automata, and finite difference/finite element, in the context of how these methods are used --- and new methods developed --- to treat real problems in physics and in other areas. Examples of such problems include study of the solar system, oscillatory motion and chaos, earthquakes and forest fire, wave propagation, percolation and fractals, phase transitions, random processes, particle transport (e.g., in space exploration or in accelerator physics), and protein folding.

The course is for graduate students in Applied Science, Physics and related disciplines. It assumes knowledge of calculus and introductory physics. Extensive computer background is not required; homework and course projects are designed to facilitate a steady accumulation of hands-on experience.

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Preliminary course outline:

• Basics. (4 lectures)
  Probability distribution and characterization; random numbers; basic Monte Carlo sampling; the central limit theorem and characterization of errors; random walks and diffusion; particle transport simulations.

• Applications of stochastic methods. (6 lectrues)
  Markov chains and the Metropolis algorithm; Monte Carlo integration; phase transitions (melting); simulated annealing and the traveling salesman problem; protein folding; quantum mechanics by random walks.

• Computer modeling and simulations. (5 lectures)
  fractals; percolation and renormalization group; cellular automata; forest fire; earthquakes; game of life.

• Newton's laws in real life --- finite-difference and related methods. (6 lectures)
  bicycle racing; baseball; golf; the solar system; molecular dynamics; properties of a dilute gas; the melting transition again.

• Potentials, fields, and waves. (3 lectures)
  Electric potentials and fields; potentials and fields near charges; motion of a string; fluid and traffic flow.

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Textbook: On reserve

H. Gould and J. Tobochnik, An introduction to computer simulation methods: applications to physical systems, 2nd edition, Addison-Wesley, 1996.

Books on reserve in Physics Library:

M.T.Heath, Scientific computing : an introductory survey, New York : McGraw-Hill, c1997.

N.J.Giordano, Computational Physics, Prentice Hall, 1997.

M.H. Kalos and P.A. Whitlock, Monte Carlo Methods, Vol I, Wiley, 1986. General reference on Monte Carlo. Probability, sampling, tricks, Metropolis, Monte Carlo methods for quantum systems.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes -- the Art of Scientific Computing, Cambridge. Contains all kinds of subroutines and discussions. Widely used in the scientific community.

P.L. DeVries, A first course in computational physics, Wiley, 1994. Good textbook. Slightly more on the numerical analysis side.

A. L. Garcia, Numerical Methods for Physics, Prentice Hall, 1994. Another text-book type of general reference.

M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids, Oxford, 1987. General introduction to classical molecular dynamics and Monte Carlo as applied to liquids.

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Grade: (not entirely based on a curve!)

• 60% --- homework (6 sets)
• 10% --- classroom participation and overall effort
• 15% --- mid-term take-home
• 15% --- final project and oral presentation

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Computing:

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• Some things to note when computing.
  • Always 'nice' your jobs, e.g., 'nice executable_name &' in unix. Use the maximum level (lowest priority) for any job that you expect to run more than a few minutes. Do 'man nice' to find out how.

  • Heavy number crunching should not be done on departmental servers (e.g., 'dm in Applied Science).

  • If you need to use xmaple on spiffy, please:
    • avoid busy hours;
    • look around (e.g., with the command 'top') and see how much is going on before deciding to launch a session.

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Your comments and suggestions are appreciated.

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