CGN 3421  Computer Methods
Gurley
Numerical Methods  Lecture 1
page 47 of 53
Numerical Methods  Lecture 1
Topics:
Numerical Methods Introduction
WHY ARE WE STUDYING THIS???
matrix methods
curve fitting
root finding
optimization
statistical analysis
probability analysis
integration / differentiation
ordinary differential equations
signal processing
NUMERICAL METHODS (why?)
Our creations are based on mathematical models
of what occurs in nature.
•
Structural response to wind/waves/earthquakes
•
Airplane performance
•
Chemical reactions
•
Automobile suspensions
•
Steel bridge deformation under heavy railroad loads
•
Traffic patterns for infrastructure design
•
Maximum capacity of piles holding up foundations
•
Waste water treatment plants
•
The betting line on Florida vs. Florida State
•
Insurance premiums
•
......
These mathematical models of physical processes allow us to design and build new creations that account
for the various stresses they will see. Without numerical methods (the creation and application of
mathematical models), there would be no aircraft, tall buildings, long bridges, etc.
We’ll look at a brief introduction of each of the topics to be covered.
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View Full DocumentCGN 3421  Computer Methods
Gurley
Numerical Methods  Lecture 1
page 48 of 53
Matrix methods  solving simultaneous equations
•
We’re familiar with the equation relating force and displacement for a spring as
.
•
We’ve also learned how to analyze a simple truss structure in statics
•
All a truss is permitted to do is stretch or compress. So one way of analyzing truss type structures is to
visualize the structure as a group of attached springs. For example, the simple truss below can be repre
sented as springs.
•
Usually engineers know what the constant
is for each spring, and the forces
acting on the structure.
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 Spring '08
 Long
 Numerical Analysis, Truss, Gurley

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