HW

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note

my score

1

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Curve fitting using least square for the blast problem

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2

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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

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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

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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

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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

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

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7

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

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8

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Minimization with constraint, Auxiliary Lagrangian method

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9

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

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10

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

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11

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

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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.

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13

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

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14

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15

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

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