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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.
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Editorial Reviews

From the Publisher
"...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 1
Pt. 1 Simple Models in Mechanics 5
1 Newtonian mechanics 7
2 Kinematics on a line 21
3 Ropes and pulleys 41
4 Friction 60
5 Differential equations: linearity and SHM 71
6 Springs and oscillations 85
Pt. 2 Models with Difference Equations 103
7 Difference equations 105
8 Linear difference equations in finance and economics 126
9 Non-linear difference equations and population growth 146
10 Models for population genetics 177
Pt. 3 Models with Differential Equations 201
11 Continuous growth and decay models 203
12 Modelling heat flow 232
13 Compartment models of mixing 257
Pt. 4 Further Mechanics 275
14 Motion in a fluid medium 277
15 Damped and forced oscillations 295
16 Motion in a plane 318
17 Motion on a circle 336
Pt. 5 Coupled Models 353
18 Models with linear interactions 355
19 Non-linear coupled models 379
References 399
Index 403
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