UsEGM6321.F10.TEAM1.WILKS/Mtg3

From Wikiversity
Jump to navigation Jump to search

EGM6321 - Principles of Engineering Analysis 1, Fall 2009


Mtg 3: Thur, 27 Aug 09

Page 3-1

[edit]

To find class homepage, go to Wikiversity: Main Page (http://en.wikiversity.org/wiki/Wikiversity:Main_Page) and search for--> user:egm6321.f09

My Wiki address is: http://clesm.mae.ufl.edu/wiki.vq/index.php/Main_Page

From Eq.(1)p.2-3: If , divide throughout by to get:

(1)



Where:

is defined as "for all"

,

,

, and



such that then is a regular point

Any such that is a regular point

EGM6321 F10 TEAM1 WILKS xc mtg3 1.svg













Page 3-2

[edit]

2nd order--> need 2 conditions to solve for 2 constraints

Boundary Value Problem (BVP)

Prescribe:

(1)


(1)

where and are known values

Initial Value Problem (IVP)

Prescribe:

(2)


(2)



where and are known values

Solve IVP by ODE from p3-1 Eq(1) or initial condition p3-2 Eq(2)

Two points:

1) Existence and uniqueness of solution

EGM6321 F10 TEAM1 WILKS Exc mtg3 2.svg













Page 3-3

[edit]

2) Superposition based on linearity of differential operation L(.)

(1)


(2)



Where the 2 in is defined as 2nd order

Linearity of

(3)



in a function of x
and belonging to (scalars, real numbers);

Where is defined as a set of real numbers

Example: Matrix Algebra

matrix with n rows and m columns of real numbers

is a column matrix


Page 3-4

[edit]

Clearly:

Example:
is a linear operation



linearity allows the use of superposition



, where the subscripts H and P stand for homogeneous and particular in respective order.

References[edit]