An Introduction to Mathematical Modeling,9780486411804

An Introduction to Mathematical Modeling

by
ISBN13: 9780486411804
ISBN10: 048641180X
Format: Paperback
Pub. Date: 2000-03-06
Publisher(s): Dover Publications
List Price: $16.95

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Summary

Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond pure mathematics needed to set up and manipulate mathematical models. From a diversity of fields-including science, engineering, and operations research-come over 100 reality-based examples. Accessible text assumes only elementary calculus, basic probability theory for first part; ordinary differential equations, continuous probability for second. Numerous references. 1978 edition. 27 black-and-white figures.

Table of Contents

What Is Modeling
1(16)
Models and Reality
1(1)
Properties of Models
2(4)
Building a Model
6(2)
An Example
8(2)
Another Example
10(4)
Problems
12(2)
Why Study Modeling?
14(3)
PART 1. ELEMENTARY METHODS 17(120)
Arguments from Scale
19(25)
Effects of Size
19(15)
Cost of Packaging
19(3)
Speed of Racing Shells
22(4)
Size Effects in Animals
26(3)
Problems
29(5)
Dimensional Analysis
34(10)
Theoretical Background
35(2)
The Period of a Perfect Pendulum
37(1)
Scale Models of Structures
38(2)
Problems
40(4)
Graphical Methods
44(22)
Using Graphs in Modeling
44(1)
Comparative Statics
45(12)
The Nuclear Missile Arms Race
45(4)
Biogeography: Diversity of Species on Islands
49(3)
Theory of the Firm
52(4)
Problems
56(1)
Stability Questions
57(9)
Cobweb Models in Economics
57(3)
Small Group Dynamics
60(3)
Problems
63(3)
Basic Optimization
66(25)
Optimization by Differentiation
66(15)
Maintaining Inventories
66(5)
Geometry of Blood vessels
71(2)
Fighting Forest Fires
73(3)
Problems
76(5)
Graphical Methods
81(10)
A Bartering Model
81(3)
Changing Environment and Optimal Phenotype
84(4)
Problems
88(3)
Basic Probability
91(30)
Analytic Models
91(12)
Sex Preference and Sex Ratio
91(3)
Making Simple Choices
94(4)
Problems
98(5)
Monte Carlo Simulation
103(18)
A Doctor's Waiting Room
106(2)
Sediment Volume
108(2)
Stream Networks
110(5)
Problems
115(3)
A Table of 3000 Random Digits
118(3)
Potpourri
121(16)
Desert Lizards and Radiant Energy
121(3)
Are Fair Election Procedures Possible?
124(3)
Impaired Carbon Dioxide Elimination
127(3)
Problems
130(7)
PART 2. MORE ADVANCED METHODS 137(80)
Approaches to Differential Equations
139(5)
General Discussion
139(1)
Limitations of Analytic Solutions
140(1)
Alternative Approaches
140(2)
Topics Not Discussed
142(2)
Quantitative Differential Equations
144(29)
Analytical Methods
144(16)
Pollution of the Great Lakes
144(4)
The Left Turn Squeeze
148(4)
Long Chain Polymers
152(3)
Problems
155(5)
Numerical Methods
160(13)
Towing a Water Skier
160(4)
A Ballistics Problem
164(1)
Problems
165(6)
The Heun Method
171(2)
Local Stability Theory
173(29)
Autonomous Systems
173(2)
Differential Equations
175(18)
Theoretical Background
175(2)
Frictional Damping of a Pendulum
177(3)
Species Interaction and Population Size
180(4)
Keynesian Economics
184(3)
More Complicated Situations
187(1)
Problems
188(5)
Differential-Difference Equations
193(6)
The Dynamics of Car Following
193(5)
Problems
198(1)
Comments on Global Methods
199(3)
Problem
201(1)
More Probability
202(15)
Radioactive Decay
202(2)
Optimal facility Location
204(3)
Distribution of Particle Sizes
207(5)
Problems
212(5)
APPENDIX. SOME PROBABILISTIC BACKGROUND 217(22)
A.1. The Notion of Probability
217(3)
A.2. Random Variables
220(4)
A.3. Bernoulli Trials
224(1)
A.4. Infinite Event Sets
225(5)
A.5. The Normal Distribution
230(2)
A.6. Generating Random Numbers
232(2)
A.7. Least Squares
234(3)
A.8. The Poisson and Exponential Distributions
237(2)
References 239(10)
A Guide to Model Topics 249(4)
Index 253

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