Simulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.
Author(s): Alfio Quarteroni
Publisher: Springer
Year: 2022
Language: English
Pages: 135
City: Cham
Preface
Acknowledgements
Contents
List of Figures
1: The Model, aka the Magic Box
1.1 Initial Data
1.2 Approximate in Order to Solve
1.3 How Many Models for One Problem? How Many Problems for a Single Model?
1.4 The Phases of a Model
2: Weather Forecast Models
2.1 A Model Based on … Thin Air
2.2 The Physical Quantities Relevant to Meteorology
2.3 Physics Comes to the Rescue
2.4 The Initial Data and the Boundary Data
2.5 Numerical Models, from D-Day to von Neumann
2.6 Increasingly Sophisticated Models: Lorenz’s Butterflies
2.7 Weather Forecasting Today
References
3: Epidemics: The Mathematics of Contagion
3.1 Preys and Predators
3.2 The Epidemiological Models
3.3 The Population’s Critical Size: The Case of Measles
3.4 A World of Susceptible Individuals
3.5 The Equations of the Contagion
3.6 The Peak, the Plateau, the Breakneck Slopes (and the Climb-Ups)
References
4: A Mathematical Heart
4.1 How Does the Cardiovascular System Work? An Eternal Challenge for Philosophers, Doctors, and Mathematicians
4.2 The Models Today
4.3 Mathematics in the Operating Room
4.4 The Blood’s Equations
4.5 At the Heart of the Problem
References
5: Mathematics in the Wind
5.1 A Sports Trophy with a Glorious History
5.2 The Swiss Outsider and the Mathematics of Sails
5.3 The Numerical Simulations
5.4 How Did It End Up?
References
6: Flying on Sun Power
6.1 The Piccards, a Family of Explorers
6.2 Ending the Fossil-Fuel Era
6.3 The Solar Impulse Mission: The Challenges
6.4 Mathematics Comes into Play
6.5 Multidisciplinary Optimisation
6.6 An Example of Multi-objective Optimisation
References
7: The Taste for Mathematics
7.1 Food Preparation
7.2 Mathematics and the Brain
7.3 The “Formula of Flavour”
7.4 Optimising the Industrial Production of Food
7.5 Mathematical Packaging
7.6 Mathematics and Health
References
8: The Future Awaiting Us
Reference
