up

My Math 503(Mathematical modeling). California State University, Fullerton. summer, 2007

Nasser M. Abbasi

summer 2007 page compiled on September 1, 2015 at 2:47am

1 Introduction

I took this course during summer 2007, at California state univ. Fullerton. This was a required course for my MSc. In Applied Mathematics.

Instructor and course official web site here

  B.S., Ph.D., Cornell University.
  Office: MH-180
  Phone: 278-3184
  Email: wgearhart@fullerton.edu

PIC

PIC

2 HW's





HW

my solution

note

my score





1

PDF HTML

Curve fitting using least square for the blast problem

2/2





2

PDF HTML

Dimensional analysis. Reduce an ODE to dimensionless form . Find ODE for ball problem with IC, then reduce ODE to dimensionless form.

2/2





3

PDF HTML

Find general solution to second oder ODE using methods of undetermined coefficients and method of variation of parameters. Wronskian formula, Verification of answer using Mathematica

2/2





4

PDF HTML

Finding stationary solution to functional Dirichlet boundary conditions, use variational method J(y + v )   . Another one to find surface of revolution (the cosh   problem). Another minimization problem (the Utility problem).

2/2





5

PDF HTML

Minimization of functional, free boundary conditions (t)   general method. Minimzation of functional with extra G (.)   function after the integral. Using (t)   method.

2/2





6

HTML

Pendulum pulled up and pendulum on hoop. Simulation using Mathematica Manipulate

2/2





7

PDF HTML

Finding expression which minimizes energy in string, weak solution. Show that classical solution implies weak solution.

2/2





8

PDF HTML

Minimization with constraint, Auxiliary Lagrangian method

2/2





9

PDF HTML

Minimization of functional over 2D. defined and free boundaries. Uses Green theorem. Normal to surface.

2/2





10

PDF HTML

Sturm Liviouel problems, finding eigenvalues and eigenfunctions, periodic B.C.

2/2





11

PDF HTML

Green Function. Using the formula method and using property method. 2 problem, both BVP

2/2





12

HTML grade

Computer assignment. Analytical part. Show  ′
J (y;h) = 0   implies minimum functional. Derive  ′
J(y;h)   from given functional. Also FEM and Central difference implementation for solving simple second order ODE.

25/25





13

PDF HTML

Finding fundamanetal solution to second order ODE using distribution method. With Mathematica Animation

2/2





14

PDF HTML

2/2





15

PDF HTML

Using energy balance equation to find PDE. Using First Green function formula to show unique solution for PDE, energy method.

2/2