# University of Florida/Egm6341/s11.TEAM1.WILKS/Mtg3

## EGM6321 - Principles of Engineering Analysis 1, Fall 2010[edit | edit source]

**Mtg 3:** Thur, 26 Aug 10

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NOTE: - page numbering 3-1 defined as meeting number 3, page 1

- T = torque Fig.p.1-1

- HW*

Eq.(3)P.2-1 : "Ordinary" Differential Equation (ODE)

order = highest order of derivative

Nonlinearity = What is linearity? ; use intuition for now, formal definition soon.

System has 3 unknowns:

Partial Differential Equations (PDE)

3 equations are coupled Numerical Methods

Simplify for analytical solution Ref:VQ&O 1989

2nd Order 2nd Order

nonlinear linear

unknown varying coefficient known varying coefficient

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Note: Math structure of coefficient for
is known, but not their values until and are known (solved for)

General structure of Linear 2nd order ODEs with varying coefficients (L2_ODE_VC)

(1) |

where

independant variable

dependant variable (unknown function to solve for)

Many applications in engineering are a result of solving PDEs by separation of variables. Some examples include, but are not limited to: Heat, Solids, Fluids, Acoustics and electrmagnetics.

Examples of these types equations are:

the Helmholz equation:

and the Laplace Equation:

Ref F09 Mtg.28, Ref F09 Mtg.29
, Ref F09 Mtg.30

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In 3_D,

(1) |

Where the lowercase in the first term is defined as

and is the separation of variables

(2) |

Where in the first term is defined as

and is the separation of variables

Separated equations for

(3) |

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Simplify:

Eq.(3)p.3-3:

(1) |

Where

Particular case of Eq.(1)p.3-2

Linearity: Let be an operator.

and are 2 possible arguments (could be functions) of

Where and are any arbitrary number.