EGM6321 - Principles of Engineering Analysis 1, Fall 2009
Mtg 3: Thur, 27 Aug 09
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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:
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(1)
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Where:
is defined as "for all"
,
,
, and
such that then is a regular point
Any such that is a regular point
2nd order--> need 2 conditions to solve for 2 constraints
Boundary Value Problem (BVP)
Prescribe:
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(1)
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(1)
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where and are known values
Initial Value Problem (IVP)
Prescribe:
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(2)
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(2)
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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
2) Superposition based on linearity of differential operation L(.)
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(1)
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(2)
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Where the 2 in is defined as 2nd order
Linearity of
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(3)
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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
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.