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
HW 
my solution 
note 
my score 
1 
Curve ﬁtting using least square for the blast problem 
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2 
Dimensional analysis. Reduce an ODE to dimensionless form . Find ODE for ball problem with IC, then reduce ODE to dimensionless form. 
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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 
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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). 
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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. 
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6 
Pendulum pulled up and pendulum on hoop. Simulation using Mathematica Manipulate 
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7 
Finding expression which minimizes energy in string, weak solution. Show that classical solution implies weak solution. 
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8 
Minimization with constraint, Auxiliary Lagrangian method 
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9 
Minimization of functional over 2D. deﬁned and free boundaries. Uses Green theorem. Normal to surface. 
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10 
Sturm Liviouel problems, ﬁnding eigenvalues and eigenfunctions, periodic B.C. 
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11 
Green Function. Using the formula method and using property method. 2 problem, both BVP 
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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. 
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13 
Finding fundamanetal solution to second order ODE using distribution method. With Mathematica Animation 
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14 

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15 
Using energy balance equation to ﬁnd PDE. Using First Green function formula to show unique solution for PDE, energy method. 
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