PHYS 302

PHYS 302
Computational Physics

Course Description

This course provides an introduction to modern tools and techniques in computational physics. Although a considerable variety of topics are covered, this is a depth-first course; students will become familiar with the details of (1) formulating problems in a fashion suitable for computation (2) formulating and applying algorithms to solve such problems and (3) performing error analysis of problem solutions. A key goal of the course is to provide students with the skills needed to effectively solve new problems computationally. Students will be assumed to be proficient in some programming language, and, although there will be a significant programming component to the course, this is not a course in programming per se. Modern software tools and environments will be used throughout the course (in labs, and in problem sets), and students will become proficient in their use, extension and interconnection.

Course Assessment

Students will be evaluated using their performance on (1) periodic homework assignments (5 throughout the term) (50%), (2) midterm and final exams (30%), and (3) a term project (20%). The homework assignments form the crucial core of the course, successful completion will require mastery of concepts and techniques covered in the lectures. Examinations will test knowledge of essential factual material, as well as the student's ability to formulate computational solutions of new problems. Wherever possible, the term project will be in an area of computational physics (or related discipline) of the student's own choosing, and is expected to require roughly as much time as 2-3 homework assignments.

Course Outline:

Unix: 1.5 weeks

Week 1: Overview, Unix basics (filesystems, commands, standard I/O, X-interface ...)

Week 2: Basic shell programming and Web authoring.

Scientfic Programming using Maple: 2.5 weeks

Week 2: Introduction, command-line and GUI interfaces, basic commands and interactive problem solving.

Week 3: Basic Maple programming.

Week 4: Intermediate Maple programming with applications.

Scientific Programming using a General Purpose Programming Language: 3 weeks

Week 5: Use of target language (Fortran 77/90, C, C++, Java, ...) in Unix environment (compilation, linking, make, RCS ...), basic programming elements (variables, basic statement types, control structures ...)

Week 6: Modularization (functions/subroutines), arrays and other data structures useful in scientific programming.

Week 7: Integration and interaction of programs with other tools (plotting packages, visualization packages, Maple ...), porting and testing codes on different architectures/machines.

Solution of Linear Systems: 1 week

Week 8: The LU decomposition algorithm, using "canned" software for solving full linear systems, applications (circuit analysis ...)

Elementary Finite Difference Methods: 2 weeks

Week 9: The nature of discrete equations derived from continuum systems, expected behaviour of FD approximations (convergence & accuracy), polynomial interpolation.

Week 10: Numerical differentiation and numerical integration, applications

Non-linear Equations (Root Finding): 1 week

Week 11: Bisection (binary search), Newton's method, Newton's method for systems of non-linear equations.

Solution of ODEs: 1 week

Week 12: Using "canned" software to solve ODEs and simple systems of ODEs.

Random Numbers, Monte Carlo and Stochastic Methods: 1 week

Week 13: Random number generators, generating non-uniformly distributed random numbers, simple Monte Carlo simulations (diffusion limited aggregation ...).