Computational Physics with Numerical Recipes
Physics 4480 / 7680, Astro 7690, Spring 2014
Monday, Wednesday, Friday 12:20-1:10, Rockefeller 104
Instructor: James Sethna, 5-5132, firstname.lastname@example.org
This course teaches the theoretical underpinnings of the methods used by
physicists and engineers in numerical computations. It follows closely the
excellent text Numerical Recipes. We will cover roughly one
chapter per week, with one exercise per chapter, and some associated
Scientific Topics (Numerical Recipes chapters)
There are three main reasons that serious computational physicists and engineers
should know this material, even though computational environments like Octave,
Python, Matlab©, and Mathematica© provide "black-box" routines that
will reliably and efficiently perform many of these tasks.
- Solution of Linear Algebraic Equations
- Interpolation and Extrapolation
- Integration of Functions
- Evaluation of Functions
- Random Numbers
- Root Finding and Nonlinear Sets of Equations
- Minimization or Maximization of Functions
- Fast Fourier Transform
- Fourier and Spectral Applications
- Statistical Description of Data
- Modeling of Data
- Classification and Inference
- Integration of Ordinary Differential Equations
- Two-Point Boundary Value Problems
- Partial Differential Equations
We will deviate from the text in that we do not expect the students
to program in C++ using the routines provided by Numerical Recipes. Rather,
we encourage them to make use of the same tools they intend to use in their
later research - either use one of the interactive computational
environments (Python, Octave, Matlab©, Mathematica©, R, ...) or
professionally written software libraries (GNU, Netlib, IMSL, NAG, ...).
A substantial portion of the course will be devoted to group projects.
- The black boxes often fail just where the physics is most interesting.
Knowing how they work is crucial for finding replacements.
- For computationally intensive tasks, one can often make use of
(or design new) specialized routines that outperform the general-purpose
- Amazingly often, researchers will use their knowledge of algorithms
to apply the basic ideas in a completely new context.
Numerical Recipes, the Art of Scientific
Computing, Third Edition,
William H. Press, Saul A. Teukolsky, William T. Vetterling, and
Brian P. Flannery, Cambridge University Press, 2007.
available at Cornell.
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