Mathematical Modelling in Real Life Problems

This book is intended to be a useful contribution for the modern teaching of applied mathematics, educating Industrial Mathematicians that will meet the growing demand for such experts.

It covers many applications where mathematics play a fundamental role, from biology, telecommunications, medicine, physics, finance and industry. It is presented in such a way that can be useful in Modelation, Simulation and Optimization courses, targeting master and PhD students. Its content is based on many editions from the successful series of Modelling Weeks organized by the European Consortium of Mathematics in Industry (ECMI). Each chapter addresses a particular problem, and is written in a didactic way, providing the description of the problem, the particular way of approaching it and the proposed solution, along with the results obtained.

All problems are real world problems. A wide range of both mathematical techniques and applications, and thus one can find problems suitable for any mathematical background The structure of each chapter as "posed problem" and "proposal of solution" is of great value for teachers that would like to drive modelling seminars, and students that would like to see applications of familiar mathematical tools to exciting real problems

Contenu

Inverse Problems in Diffuse Optical Tomography Applications.- 1D Models for Blood Flow in Arteries.- Uncertainty Quantificatio of Chemical Kinetic Reaction Rate Coefficients.- Nuclear Accidents: How Can Mathematicians Help to Save Lives?.- Drug Delivery from Ophthalmic Lenses.- The Zombie Invasion.- Optimal Heating of an Indoor Swimming Pool.- Some Basic Epidemic Models.- Mathematical Model for the Game Management Plan.- Efficient Parameter-Dependent Simulation of Infections in a Population Model.- Optimising a Cascade of Hydro-electric Power Stations.- Networks of Antennas: Power Optimization.