Modelling with Differential and Difference Equations

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Overview

The theme of this book is modeling the real world using mathematics. 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. Among the broad spectrum of topics studied in this book are: mechanics, genetics, thermal physics, economics and population studies.
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Editorial Reviews

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"...highly recommended...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." G.J.F. Junevicus, Choice

"If you are looking for a textbook for an introdutory course on mathematical modeling, with an emphasis on differential and difference equations and basic calculus as the only prerequisite, then give this book serious consideration. It is very well written and very well structured.... overall presentation of material is excellent.... an excellent reference for anyone who has an interest in mathematical modeling....The foundation that this text helps to build will easily allow the reader to move on to more advanced texts on mathematical modeling." The UMAP Journal

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Product Details

Table of Contents

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.
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