MA3264 Mathematical Modelling Lecture 2

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MA3264 Mathematical ModellingLecture 2

• The Modelling Process

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Real and Mathematical Worlds
System assemblage of interacting objects
Mathematical Model graphical, symbolic,
simulation, and experimental constructs designed
to study a particular system
Equations, Rules, Computations
Observed Behavior
System
Model
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Model Attibutes
Fidelity how precise ?
Cost how much time, money, effort ?
Flexibility ability to change and control ?
Question why are tradeoffs required ?
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Model Construction
Activity
Steps
1. Identify Problem
2. Make Assumptions
a. Classify variables independent dependent
b. Determine their interrelationships
3. Solve / interpret the model
4. Verify the model
5. Implement the model
6. Maintain the model
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Vehicular Stopping Distance p.59-61
Identify Problem Predict the vehicles total
stopping distance d as a function of its speed.
Assumption
where
where
Question What forms may the functions f and h
have ?
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Vehicular Stopping Distance p.59-61
Question What shape will the graph of D(S) have ?
Experiment Plot the data on page 71 and compare
with the model on page 72
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Famous Proportionalities p. 67
Extra Topic Harmonic Motion
Hookes Law Newtons Law Acceleration
?
?
Question What are
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Raindrops p. 77
Question Why does
Question When does
Question What is
Question How does terminal velocity depend on
mass ?
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Suggested ReadingProblems in Textbook
Introduction pages 52-63, problems 5, 8, 9 on
page 63
Example 1 on pages 67-68 Keplers Third Law
Problem 2 page 74
Example 1 on pages 77-78
Problems 2 on pages 85-86
NOTE These problems are NOT to be handed in nor
will they be discussed during tutorial they are
only intended as a learning excercise
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Tutorial 2 Due Week 1-5 September
Page 63 Problem 5
Page 74 Problem 4
Page 75 Problems 5, 6
Page 87 Problem 5