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

summer 2007   Compiled on October 26, 2018 at 9:09am  [public]

### 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

### 2 HW’s

 HW my solution note my score 1 Curve ﬁtting using least square for the blast problem 2/2 2 Dimensional analysis. Reduce an ODE to dimensionless form . Find ODE for ball problem with IC, then reduce ODE to dimensionless form. 2/2 3 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 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 Minimization of functional, free boundary conditions $$\phi (t)$$ general method. Minimzation of functional with extra $$G(.)$$ function after the integral. Using $$\phi (t)$$ method. 2/2 6 Pendulum pulled up and pendulum on hoop. Simulation using Mathematica Manipulate 2/2 7 Finding expression which minimizes energy in string, weak solution. Show that classical solution implies weak solution. 2/2 8 Minimization with constraint, Auxiliary Lagrangian method 2/2 9 Minimization of functional over 2D. deﬁned and free boundaries. Uses Green theorem. Normal to surface. 2/2 10 Sturm Liviouel problems, ﬁnding eigenvalues and eigenfunctions, periodic B.C. 2/2 11 Green Function. Using the formula method and using property method. 2 problem, both BVP 2/2 12 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 Finding fundamanetal solution to second order ODE using distribution method. With Mathematica Animation 2/2 14 2/2 15 Using energy balance equation to ﬁnd PDE. Using First Green function formula to show unique solution for PDE, energy method. 2/2