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Mathematical Modelling

  • Textbook
  • © 2016

Overview

Authors:
  1. Matti Heiliö

    1. School on Engineering Science, Lappeenranta University of Technology, Lappeenranta, Finland

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  2. Timo Lähivaara

    1. Department of Applied Physics, University of Eastern Finland, Kuopio, Finland

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  3. Erkki Laitinen

    1. Department of Mathematical Sciences, University of Oulu, Oulu, Finland

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  4. Timo Mantere

    1. Department of Computer Science, University of Vaasa, Vaasa, Finland

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  5. Jorma Merikoski

    1. School of Information Sciences, University of Tampere, Tampere, Finland

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  6. Seppo Pohjolainen

    1. Department of Mathematics, Tampere University of Technology, Tampere, Finland

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  7. Kimmo Raivio

    1. Huawei Technologies, Helsinki, Finland

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  8. Risto Silvennoinen

    1. Department of Mathematics, Tampere University of Technology, Tampere, Finland

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  9. Antti Suutala

    1. Department of Mathematics, Tampere University of Technology, Tampere, Finland

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  10. Tanja Tarvainen

    1. Department of Applied Physics, University of Eastern Finland, Kuopio, Finland

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  11. Timo Tiihonen

    1. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

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  12. Jukka Tuomela

    1. Department of Physics and Mathematics, University of Eastern Finland, Joensuu, Finland

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  13. Esko Turunen

    1. Department of Mathematics, Tampere University of Technology, Tampere, Finland

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  14. Marko Vauhkonen

    1. Department of Applied Physics, University of Eastern Finland, Kuopio, Finland

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Editors:
  1. Seppo Pohjolainen

    1. Tampere University of Technology Department of Mathematics, Tampere, Finland

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  • Covers the most important classical and modern methods of mathematical modelling

  • Can be used as textbook or as complimentary material in mathematical modelling courses

  • Contains 31 project titles as well as 124 problems sets

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • Seppo Pohjolainen, Matti Heiliö
    Pages 1-5

  3. Models and Applications

    • Matti Heiliö
    Pages 7-23

  4. Viewpoints on Systems and Models

    • Erkki Laitinen
    Pages 25-34

  5. Integer Models

    • Risto Silvennoinen, Jorma Merikoski
    Pages 35-54

  6. Data Based Models

    • Jorma Merikoski
    Pages 55-78

  7. Soft Computing Methods

    • Esko Turunen, Kimmo Raivio, Timo Mantere
    Pages 79-112

  8. Dimensional Analysis

    • Timo Tiihonen
    Pages 113-121

  9. Modelling with Differential Equations

    • Jukka Tuomela
    Pages 123-148

  10. Continuum Models

    • Timo Tiihonen
    Pages 149-170

  11. Simplification of Models

    • Timo Tiihonen
    Pages 171-183

  12. Acoustic Modelling

    • Seppo Pohjolainen, Antti Suutala
    Pages 185-205

  13. Inverse Problems

    • Marko Vauhkonen, Tanja Tarvainen, Timo Lähivaara
    Pages 207-227

  14. Project Titles

    • Matti Heiliö
    Pages 229-237

  15. Back Matter

    Pages 239-242
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Keywords

About this book

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.  



                        

Reviews

“Mathematical modelling is a product of several different contributors, all from Finnish universities. The result is a text used by over 2,000 students. … This is an excellent book, written with a myriad of interesting and very practical problems and applications. The contributors to the text are obviously scientific scholars who are elegantly educated.” (James Van Speybroeck, Computing Reviews, March, 2017)  

  

Authors, Editors and Affiliations

  • Tampere University of Technology Department of Mathematics, Tampere, Finland

    Seppo Pohjolainen

  • School on Engineering Science, Lappeenranta University of Technology, Lappeenranta, Finland

    Matti Heiliö

  • Department of Applied Physics, University of Eastern Finland, Kuopio, Finland

    Timo Lähivaara, Tanja Tarvainen, Marko Vauhkonen

  • Department of Mathematical Sciences, University of Oulu, Oulu, Finland

    Erkki Laitinen

  • Department of Computer Science, University of Vaasa, Vaasa, Finland

    Timo Mantere

  • School of Information Sciences, University of Tampere, Tampere, Finland

    Jorma Merikoski

  • Department of Mathematics, Tampere University of Technology, Tampere, Finland

    Seppo Pohjolainen, Risto Silvennoinen, Antti Suutala, Esko Turunen

  • Huawei Technologies, Helsinki, Finland

    Kimmo Raivio

  • Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Timo Tiihonen

  • Department of Physics and Mathematics, University of Eastern Finland, Joensuu, Finland

    Jukka Tuomela

About the editor

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. 

 


                          

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