A Primer on Mathematical Modelling

In this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers.

A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites.

This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasio This book is addressed to any student interested in learning how to construct and apply mathematical models.

Addresses real-life problems and their solutions using mathematical and numerical models A gym for interdisciplinary skills (mathematics, physics, life sciences, computer science) Discusses programming in Octave

Auteur

Paola Gervasio completed her PhD in Mathematics at the University of Milan (Italy) in 1995, and she has been an Associate Professor of Numerical Analysis at the University of Brescia (Italy) since 2005. She is the author of 4 books and of about 40 papers. Her research focuses on the approximation of partial differential equations by high-order methods and domain decomposition techniques, particularly in the context of multi-physics problems.

Alfio Quarteroni is a Professor of Numerical Analysis at Politecnico of Milan and Professor Emeritus at EPFL of Lausanne. He is the author of 25 books and about 400 papers, and editor of 9 books. He is the recipient of two ERC Advanced Grants; the Galileian Chair from the Scuola Normale Superiore, Pisa; the Galileo international prize for Science; and an honorary doctorate in Naval Engineering from the University of Trieste. He is member of the Italian Academy of Science, the European Academy of Science, the Academia Europaea, and the Lisbon Academy of Science. His research interests include mathematical and numerical modeling for fluid mechanics, geophysics, medicine and the improvement of sports performance. His research group at EPFL carried out the mathematical simulation for the Alinghi sailing boat, which won the America's Cup in 2003 and 2007.

Résumé
"The book is extremely well written and is spectacular in its beauty. It is full with colorful pictures and figures, with many clear graphs, algorithms, codes (written in Octave) and tables, which makes reading the book a real joy. ... This is a superb book for readers doing their initial steps in the wonderful world of modeling. I recommended it to my 17-year-old nephew, who is now reading it with great enthusiasm." (Dan Givoli, IACM Expressions, Issue 50, July, 2022)
"It is thus appropriate for junior college students. It is even suitable for self-study and independent research projects. ... Professors Quarteroni and Gervasio have written a nice and fun book, which also constitutes a useful toolbox for anyone who wants to get acquainted with the methods of Applied Mathematics." (Fernando Tohmé, zbMATH 1475.00018, 2022)

"The book is an outstanding document from an educational point of view. ... The interaction of the simplicity of mathematical methods and the sophistication of the three main applications is very well done. In summary, this new book is highly recommended for both undergraduate and graduate students who are interested in mathematical modeling ... ." (Thomas Wick, SIAM Review, Vol. 63 (3), September, 2021)

Contenu

1. A warm-up to models.- 2. Getting started.- 3. Reckoning with the computer.- 4. A virtual surfer for the web.- 5. A network of capillaries.- 6. Predators and preys in the maths ocean.- 7. Take-home message.- 8. Solutions to exercises.