Synopses & 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.
Explains the relevance and importance of mathematical modelling for a non-technical audience.
Table of Contents
1. Overview; 2. Sequences and difference equations; 3. Arithmetic growth; 4. Linear graphs, functions and equations; 5. Quadratic growth models; 6. Quadratic graphs, functions and equations; 7. Polynomial and rational functions; 8. Fitting a line to data; 9. Geometric growth; 10. Exponential functions; 11. More on logarithms; 12. Geometric sums and mixed models; 13. Logistic growth; 14. Chaos in logistic models.