PHY 5157, Outline

SYLLABUS
PHY 5157, Syllabus
Fall 2000 PHY 5157 -- Advanced Numerical Applications in Physics
Instructor: Bernd A. Berg (FSU, Physics, Tel. 644-6217).

Credit
3 semester hours. The class will meet for two 90-minute periods per week. The course is part of the new computational physics master program.

Prerequisites
The course is intended for graduate students and senior undergraduate students. A working knowledge of Fortran or C is required. Students are assumed to be proficient in Calculus and to know Mechanics, Electrodynamics and Quantum Mechanics on the undergraduate level.

Objectives
The students should aquire a thorough understanding of the introduced methods. They should become able to implement the methods in their own computer programs and to present the thus obtained results.

Course Description
With the emergence of a third arm of science, known as ``high-performance computing'', one can now tackle computational physics problems that were prohibitively costly just a few years ago. The goal of the course is to introduce the students to some of the powerful numerical techniques widely used in physics. The course will focus on three major topics.

Numerical Methods for Integration and Partial Differential Equations

Statistics and Data Analysis

Stochastic Simulations
It is intended to spend approximately one third of the time on each topic. However, depending on the interests of the participants the relative weights can be changed. The last two topics will be taught in a strongly intertwinned way.

Text

Numerical Recipes by William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery, Cambridge University Press, 1993. Choose the Fortran or C edition according to you programing preferences.

Introduction to Monte Carlo Simulations and Their Statistical Analysis, script provided by the instructor.

Assessment
The course grade will be based on homework and on a final project, with each one representing 50% of the grade. Regular class attendance is mandatory, "no-shows" may count against and assignments in class towards the homework score. The course grade dividing lines on the basis of the weighted score in percent are: A > 85% , A- > 80% , B+ > 75% , B > 64% , B- > 60% , C+ > 56% , C > 44% , C- > 40% , D+> 36% , D > 24% , D- > 20% and F for less or equal 20% .

Details
1.1 Integration with Maple
1.2 Romberg Integration
1.3 Gaussian Quadrature

Examples from Mechanics, Electrodynamics and Statistical Physics will be considered.
1.4 The Runge-Kutta method for Ordinary Differential Equations
1.5 Relaxation Methods for Partial Differential Equations

Illustrations will be given for the Schrodinger equation, the Dirac equation and for diffusion.
2.1 Descriptive Statistics and Random Numbers
2.2 Chi2 Distribution and Error Analysis
2.3 Jackknife and bootstrap methods

These methods will be applied to experimental and Monte Carlo data
3.1 Importance Sampling, Heat Bath and Metropolis Monte Carlo
3.2 Autocorrelations
3.3 Generalized Ensembles
3.4 Simulated Annealing and other Optimization Methods

Computer programs will be provided or developed for Potts models in d dimensions (including the Ising model), the Heisenberg Ferromagnet and pure lattice gauge theory. Generalized ensemble methods will be illustrated for Potts models. The Traveling Saleman problem will serve to illustrate optimization techniques.

Back to the Advanced Numerical Applications in Physics Homepage.

Credit	3 semester hours. The class will meet for two 90-minute periods per week. The course is part of the new computational physics master program.
Prerequisites	The course is intended for graduate students and senior undergraduate students. A working knowledge of Fortran or C is required. Students are assumed to be proficient in Calculus and to know Mechanics, Electrodynamics and Quantum Mechanics on the undergraduate level.
Objectives	The students should aquire a thorough understanding of the introduced methods. They should become able to implement the methods in their own computer programs and to present the thus obtained results.
Course Description	With the emergence of a third arm of science, known as ``high-performance computing'', one can now tackle computational physics problems that were prohibitively costly just a few years ago. The goal of the course is to introduce the students to some of the powerful numerical techniques widely used in physics. The course will focus on three major topics. Numerical Methods for Integration and Partial Differential Equations Statistics and Data Analysis Stochastic Simulations It is intended to spend approximately one third of the time on each topic. However, depending on the interests of the participants the relative weights can be changed. The last two topics will be taught in a strongly intertwinned way.
Text	Numerical Recipes by William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery, Cambridge University Press, 1993. Choose the Fortran or C edition according to you programing preferences. Introduction to Monte Carlo Simulations and Their Statistical Analysis, script provided by the instructor.
Assessment	The course grade will be based on homework and on a final project, with each one representing 50% of the grade. Regular class attendance is mandatory, "no-shows" may count against and assignments in class towards the homework score. The course grade dividing lines on the basis of the weighted score in percent are: A > 85% , A- > 80% , B+ > 75% , B > 64% , B- > 60% , C+ > 56% , C > 44% , C- > 40% , D+> 36% , D > 24% , D- > 20% and F for less or equal 20% .
Details	1.1 Integration with Maple 1.2 Romberg Integration 1.3 Gaussian Quadrature Examples from Mechanics, Electrodynamics and Statistical Physics will be considered. 1.4 The Runge-Kutta method for Ordinary Differential Equations 1.5 Relaxation Methods for Partial Differential Equations Illustrations will be given for the Schrodinger equation, the Dirac equation and for diffusion. 2.1 Descriptive Statistics and Random Numbers 2.2 Chi2 Distribution and Error Analysis 2.3 Jackknife and bootstrap methods These methods will be applied to experimental and Monte Carlo data 3.1 Importance Sampling, Heat Bath and Metropolis Monte Carlo 3.2 Autocorrelations 3.3 Generalized Ensembles 3.4 Simulated Annealing and other Optimization Methods Computer programs will be provided or developed for Potts models in d dimensions (including the Ising model), the Heisenberg Ferromagnet and pure lattice gauge theory. Generalized ensemble methods will be illustrated for Potts models. The Traveling Saleman problem will serve to illustrate optimization techniques.