Enhanced descriptions from Syndetics:

The real world can be modelled using mathematics, and the construction of such models is the theme of this book. The authors concentrate on the techniques used to set up mathematical models and describe many systems in full detail, covering both differential and difference equations in depth. Amongst the broad spectrum of topics studied in this book are: mechanics, genetics, thermal physics, economics and population studies. Any student wishing to solve problems via mathematical modelling will find that this book provides an excellent introduction to the subject.

Table of contents provided by Syndetics

• Preface
• Introduction to the student
• Part I Simple Models In Mechanics
• 1 Newtonian mechanics
• 2 Kinematics on a line
• 3 Ropes and pulleys
• 4 Friction
• 5 Differential equations: linearity and SHM
• 6 Springs and oscillations
• Part II Models with Difference Equations
• 7 Difference equations
• 8 Linear difference equations in finance and economics
• 9 Non-linear difference equations and population growth
• 10 Models for population genetics
• Part III Models with Differential Equations
• 11 Continuous growth and decay models
• 12 Modelling heat flow
• 13 Compartment models of mixing
• Part IV Further Mechanics
• 14 Motion in a fluid medium
• 15 Damped and forced oscillations
• 16 Motion in a plane
• 17 Motion in a circle
• Part V Coupled Models
• 18 Models with linear interactions
• 19 Non-linear coupled models
• References
• Index

Reviews provided by Syndetics

CHOICE Review

In Elementary Mathematical Models, Kalman uses basic growth models (arithmetic, quadratic, geometric, mixed arithmetic-geometric, and logistic) not only to convey the power of mathematics in solving real-world problems but also to motivate the study of the elementary functions usually encountered in college algebra courses. There is a natural evolution from simple hypotheses to difference equations, to their solutions, to the study of the elementary functions associated with the solutions. There is an emphasis on the why of algebra and on manipulation associated with applications rather than for its own sake. Numerical, graphical, and symbolic approaches are used throughout, and the numerous exercises include reading comprehension exercises and group activities as well as more traditional problems. There are solutions to selected exercises. Aimed at students at the college algebra or liberal arts mathematics level, the slow, careful development should be clear even to those with a weak algebraic background. Highly recommended. Lower-division undergraduates. Modeling with Differential and Difference Equations covers a broad spectrum of models from such diverse areas as mechanics, genetics, thermal physics, medicine, economics, and population studies. For each model the relevant background theory is provided along with carefully laid out assumptions. Model development is clear and deliberate--indeed, it is algorithmic, concentrating on the techniques used to set up mathematical models. Although some familiarity with elementary linear algebra and calculus is assumed, the essential theory is provided to analyze and solve the simple differential and difference equations that arise. Introductory examples are well chosen and clearly developed, and exercises reinforce the material well; they vary from the almost trivial to those challenging the reader to develop models that are variants of those presented. Excellent references to classic works. Highly recommended. Undergraduates. Mathematical Models in the Applied Sciences differs markedly from the two books previously discussed and from most other modeling books. The models are more complex and their development is very condensed. A defining characteristic is the emphasis on advanced techniques of analysis. Such techniques as nondimensionalization, scale analysis, and perturbation theory are demonstrated to be unifying threads in the analysis of a wide array of models arising from diverse disciplines. Examples are presented from the physical, biological, physiological, environmental, and industrial sciences. The scope is uniquely broad; many models are unavailable in other modeling books; Fowler culled them from theses and research reports. The notes and references are invaluable guides to the literature, as classic works are cited. This is a demanding text; the exercises are excellent and challenging, and some are at the level of research problems. Applied mathematicians, engineers, and scientists will appreciate this book. Highly recommended. Graduates through professionals. G. J. G. Junevicus Eckerd College