Mathematical Modelling

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This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context.

The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

 

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Contents

1 Introduction
1
2 Models and Applications
7
3 Viewpoints on Systems and Models
25
4 Integer Models
35
5 Data Based Models
55
6 Soft Computing Methods
79
7 Dimensional Analysis
113
8 Modelling with Differential Equations
123
9 Continuum Models
149
10 Simplification of Models
171
11 Acoustic Modelling
185
12 Inverse Problems
207
13 Project Titles
229
Index
238
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About the author (2016)

Seppo Pohjolainen received his PhD degree in applied mathematics in 1980 from Tampere University of Technology (TUT). In 1998 he was appointed as a professor in mathematics at TUT.

His research interests include mathematical control theory, distributed parameter systems, mathematical modelling and simulation, development and use of information technology to support learning. Currently he is leading a nationwide network in Finland on teaching mathematical modelling on the Internet. He has led several national and international research projects and written a number of journal articles and conference papers on all these fields.