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1: Mathematical Modelling
1: Mathematical Modelling
Numerical Methods
Numerical Methods
and
and
Problem Solving
Problem Solving
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View Full Document September 20, 2006 13:17
2
Chapter Objectives
●
Illustrate how
mathematical models
can be developed to model simple
physical systems.
●
Demonstrate how
numerical methods
can be used to generate solutions to
mathematical models.
–
show implementation on digital computers.
●
Illustrate the
conservation laws
that form the basis of mathematical models
in engineering.
–
show differences between steadystate and dynamic solutions.
●
Introduce the different
types of numerical methods
that we will study in this
course.
September 20, 2006 13:17
3
A Simple Mathematical Model
Wish to predict velocity as a function of time.
In general:
●
Dependent variable
: a characteristic that reflects
behaviour. In our case:
v
(velocity).
●
Independent variable
: usually dimensions such as time
and space, along which behaviour is determined.
e.g.:
t
(time).
●
Parameter
: reflect system properties. e.g.: mass, drag
coeff., etc.
●
Forcing function
: external influences. e.g.: gravitational
attraction, wind resistance.
Dependent
variable
=
f
independent
variables
,
parameters
,
forcing
functions
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4
A Simple Mathematical Model (contd.)
Math. model of Newton's 2
nd
law of motion:
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This document was uploaded on 04/14/2010.
 Winter '09

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