Physics 325: Scientific Computing - Fall 2009

Location: TBA Time: TBA
Prerequisites: Calculus-I, Calculus-II, Classical Mechanics

Text: Computational Physics, by Nicholas J Giordano and Hisao Nakanishi, 2nd Edition, Prentice Hall.

Instructor: Dr. Raghani ( pushparaghani@boisestate.edu)

Office hours: Monday and Wednesday, from 2pm to 4pm

Topics:
  • Introduction to computational physics, programming concepts, Fortran 90, plotting utilities
  • Numerical Differentiation, Numerical quadrature, Finding Roots
  • Ordinary Differential Equations
    • Euler Method, Euler-Cromer method, Runge-Kutta method, Verlet Method
      Physical Problems
      • Radioactive decay
      • Projectile motion
      • Simple Harmonic motion
      • Solar System
  • Fourier Transforms
    • Fast Fourier Transform (FFT)
    • Estimation of the Power Spectrum
The evaluation will be based on the following. There will be two exams, one project - for 3 to 4 weeks, occasional quizzes and assignments. The weightage on each of the items is given below.

Quiz ----> 10%

Assignments ----> 20%

Project ------> 30%

Two exams ------> 40% (20% each)

Quiz: There will be 10 minute quizzes in the class without prior notice. They will usually be based on the ongoing topic in the class and will not require any prior preparation. you can seek clarifications from the instructor and hints will also be provided. There will not be any fixed day for the quiz, this means that you need to be present in every class and come on time so that you don't miss anything that might be helpful to do the quiz. Use of laptops is prohibited during the quiz.

Assignments: Assignments will be predominantly programming based, i.e., solving physical problems numberically. Assignments problems will be given during the lecture and will also be available on the website. Each assignment will typically consist of two to three problems. All assignments should be submitted by their due date. Assignments involving computer files (source code, graphs, tables etc.) should be submitted electronically by emailing to pushparaghani@boisestate.edu with subject phys325 (one word) and the assignment number. Written assignments should be submitted at the physics office. Plagiarism will not be tolarated. Assignments must be done individually. Late assignments will not be accepted.

Project: As a part of the course, you will be required to undertake a joint project with another student. You can propose your own project or choose from a suggested list. Project should utilize algorithms taught in the class, although not limited to those.

Exams: There will be a midterm and a final exam, each with 20% weightage. Both exams have the same weightage of 20%. The midterm exam will be after five weeks of the course.

Course grades be will be on the following percentages.

A = 87.5% - 100%,B = 75% - 87.5%,
C = 60% - 75%,D = 45% - 60%

First Week
Introduction, exams, assignments, quiz policy etc.
Introduction to computational physics
Introduction to Unix, programming, Fortran 90, plotting

Second Week
Tutorial on Fortran 90 and cygwin
Numerical differentiation: forward difference from Taylor series and from graphical representation (with secant line and tangent line)
Backward difference and central difference

Third Week
Numerical quadrature: Rectangular rule and Trapezoidal rule, explanagion of various terms in Taylor series
Error analysis in mid point rule, deriving Simpson's rule by including second order term in the series
Deriving formal equation of Sumpson's rule and error in Simpson's rule.

Fourth Week
Solving first order differential equation (Euler method): Radioactive decay problem (9/14/09)
Realistic projectile motion: Bicycle+Rider problem (9/16/09)
Bicycle+Rider problem contd., Went through Lab3 (9/18/09)

Fifth Week
Went through the assignment#1 and Lab#2 (9/21/09)
Explaining how the integers and real numbers are stored in computer memory (9/23/09)
Exam (9/25/09)

Sixth Week
Went through the exam (9/28/09)
Projectile motion: Shell shot by a cannon-no drag force (9/30/09)
Shell shot by a cannon-including drag force (10/2/09)

Seventh Week
Oscillatory motion: Ideal Pendulum-no friction, small angle (10/5/09)
Pendulum: Euler-Cromer method, adding damping and driving force (10/7/09)

Eight Week
Higher order methods: Runge-Kutta methods-2nd order (10/12/09)
Higher order methods: Runge-Kutta methods-4th order (10/14/09)
Comparison of 2nd order RK and Euler method, Planetary motion, 2-body problem (10/16/09)

Ninth Week
Planetary motion, three-body problem, introduction to arrays in fortran 90 (10/19/09)
Root finding: Newton-Raphson, Secant and Bisection methods; direct optimization (10/23/09)

Tenth Week
Data fitting: Method of least squares (10/26/09)
Monte Carlo method for integration (10/28/09)

Eleventh Week
Fourier Series (synthesis): Modeling complex periodic functions (of period 1) using sine and cosine as basic building blocks (11/2/09)
Deriving formulae for Fourier coefficients of a given signal (function) (11/4/09)
Modelling switch using Fourier series, spectrum of square wave (11/06/09)

Twelfth week
Analogy between vector and function spaces; Introducing the problem of heat flow in a ring (11/09/09)
Solving the problem of heat flow in a ring; Transition from periodic phenomena to non-periodic phenonmena (11/11/09)
Spectrum of a rectangle function; Discrete Fourier transform (11/13/09)
Quiz on spectrum of triangle function; drowning child problem (optimization problem)
Summary of Fourier Transform

Thirteenth week
Introduction to partial differential equations; Laplace equation (11/16/09)
Solving Laplace equation numerically; Jacobi relaxation method (11/18/09)
Solving Poisson's equation for a charge in a cubic box (11/20/09)

Fourteenth Week
Solving the system of linear equations using Gaussian elimination and Gauss-Jordon methods; Inverting the coefficient matrix (Boundary value problem) (11/30/09)
Project presentations by students (12/2/09)
Project presentations by students (12/4/09)

Fifteenth week
LU decomposition of matrices (12/7/09)