PHYX 5350 – Spring 2009

 

 

 

Methods of Theoretical Physics II

Semester: Spring 2009

Time: 10:30 - 11:20 MWF

 

 

Instructor: Ludger Scherliess

 

Course Objectives

 

To Understand and implement some important numerical methods used in computational physics.

 

To Gain confidence in solving problems numerically using Fortran 90.

 

Lecture Notes

 

Handouts

 

Home Work Assignments

 

 

Syllabus

 

I. Introduction

 

á  Accuracy in computing

 

á  Local interpolation and cubic splines

 

á  Definite integrals: trapezoidal rule, Romberg integration and Gaussian quadrature

 

 

II. Ordinary Differential Equations (ODE's)

 

á  Linear and Nonlinear ODE's

 

á  Initial value problems: Runge-Kutta and adaptive methods

 

á  Boundary value problems: shooting and finite-difference methods

 

 

III. Partial Differential Equations (PDE's)

 

Parabolic (diffusion), elliptic (Poisson), hyperbolic (wave/advection)

 

á  Finite-difference and finite-element spatial discretization

 

á  Explicit, semi-implicit and implicit time-stepping schemes

 

á  Stability analysis

 

 

Official Text: Handouts

 

Reference Texts:

 

Undergraduate texts

 

á  Introduction to Numerical Methods (Stark)

 

á  Applied Numerical Analysis (Gerald & Wheatley)

 

á  Numerical Methods for Physics (Garcia)

 

 

Graduate Texts:

 

á  Introduction to Numerical Analysis (Stoer & Bulirsch)

 

á  Numerical Recipes in Fortran 77 (Press, Teukolsky, Vetterling & Flannery)

 

á  Computational Methods for Fluid Dynamics (Ferziger & Peric)

 

 

 Fortran 90 References:

 

á  Upgrading to Fortran 90 (Redwine)

 

á  Intro. to Fortran 90 (Nyhoff)

 

á  An Intro. to Fortran 90 for Scientific Computing (Ortega)

  

á  Intro. to Fortran 90/95 (Chapman)

 

 

    Grading:

 

Homework            50% of total grade

Late Midterm        30% of total grade

Final Project         20% of total grade

 

 

 

   University Honor Code:

 

The honor code will be strictly enforced in this course.  Any suspected violations of the honor code will be promptly reported to the honor system. For more info, go to Discipline on the following USU website:

 

http://www.usu.edu/policies/PDF/R-MainPolicyBody-January-03.pdf

 

 

 

 

   Students with Disabilities:

 

Students with physical, sensory, emotional or medical impairments may be eligible for reasonable accommodations in accordance with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973. All accommodations are coordinated through the Disability Resource Center (DRC) in Room 101 of the University Inn, 797-2444 voice, 797-0740 TTY, or toll free at 1-800-259-2966. Please contact the DRC as early in the semester as possible. Alternate format materials (Braille, large print or digital) are available with advance notice.