Elementary Mathematical Models: Order Aplenty and a Glimpse of Chaos

Front Cover
Cambridge University Press, 1997 - Mathematics - 345 pages
0 Reviews
The language of mathematics has proven over centuries of application to be an indispensable tool for the expression and analysis of real problems. With numerical, graphical, and theoretical methods, this book examines the relevance of mathematical models to phenomena ranging from population growth and economics to medicine and the physical sciences. In a book written for the intelligent and literate non-mathematician, Kalman aims at an understanding of the power and utility of quantitative methods rather than at technical mastery of mathematical operations. He shows first that mathematical models can serve a critical function in understanding the world, and he concludes with a discussion of the problems encountered by traditional algebraic assumptions in chaos theory. Though models can often approximate future events based on existing data and quantitative relationships, Kalman shows that the appearance of regularity and order can often be misleading. By beginning with quantitative models and ending with an introduction to chaos, Kalman offers a broad treatment of both the power and limitations of quantitatively-based predictions.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Overview
1
Sequences and Difference Equations
11
Arithmetic Growth
37
Linear Graphs Functions and Equations
55
Quadratic Growth Models
79
Quadratic Graphs Functions and Equations
117
Polynomial and Rational Functions
149
Fitting a Line to Data
165
Geometric Growth
181
Exponential Functions
213
More On Logarithms
233
Geometric Sums and Mixed Models
255
Logistic Growth
287
Chaos in Logistic Models
319
Index
341
Copyright

Common terms and phrases

Bibliographic information