A concrete approach to mathematical modelling / / Michael Mesterton-Gibbons

• Autore: Mesterton-Gibbons Mike
• Pubblicazione: New York, : John Wiley & Sons, 2007
• Descrizione fisica: 1 online resource (620 p.)
• Disciplina: 511.8
• Soggetto topico: Mathematical models
• Note generali: "A Wiley-Interscience publication."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: A Concrete Approach to Mathematical Modelling; CONTENTS; An ABC of modelling; I The Deterministic View; 1 Growth and decay. Dynamical systems; 1.1 Decay of pollution. Lake purification; 1.2 Radioactive decay; 1.3 Plant growth; 1.4 A simple ecosystem; 1.5 A second simple ecosystem; 1.6 Economic growth; 1.7 Metered growth (or decay) models; 1.8 Salmon dynamics; 1.9 A model of U.S. population growth; 1.10 Chemical dynamics; 1.11 More chemical dynamics; 1.12 Rowing dynamics; 1.13 Traffic dynamics; 1.14 Dimensionality, scaling, and units; Exercises; 2 Equilibrium ; 2.1 The equilibrium concentration of contaminant in a lake2.2 Rowing in equilibrium; 2.3 How fast do cars drive through a tunnel?; 2.4 Salmon equilibrium and limit cycles; 2.5 How much heat loss can double-glazing prevent?; 2.6 Why are pipes circular?; 2.7 Equilibrium shifts; 2.8 How quickly must drivers react to preserve an equilibrium?; Exercises; 3 Optimal control and utility; 3.1 How fast should a bird fly when migrating?; 3.2 How big a pay increase should a professor receive?; 3.3 How many workers should industry employ?; 3.4 When should a forest be cut? ; 3.5 How dense should traffic be in a tunnel?3.6 How much pesticide should a crop grower use-and when?; 3.7 How many boats in a fishing fleet should be operational?; Exercises; II Validating a Model; 4 Validation: accept, improve, or reject; 4.1 A model of U.S. population growth; 4.2 Cleaning Lake Ontario; 4.3 Plant growth; 4.4 The speed of a boat; 4.5 The extent of bird migration; 4.6 The speed of cars in a tunnel; 4.7 The stability of cars in a tunnel; 4.8 The forest rotation time; 4.9 Crop spraying; 4.10 How right was Poiseuille?; 4.11 Competing species; 4.12 Predator-prey oscillations ; 4.13 Sockeye swings, paradigms, and complexity4.14 Optimal fleet size and higher paradigms; 4.15 On the advantages of flexibility in prescriptive models; Exercises; III The Probabilistic View; 5 Birth and death. Probabilistic dynamics; 5.1 When will an old man die? The exponential distribution; 5.2 When will ? men die? A pure death process; 5.3 Forming a queue. A pure birth process; 5.4 How busy must a road be to require a pedestrian crossing control?; 5.5 The rise and fall of the company executive; 5.6 Discrete models of a day in the life of an elevator ; 5.7 Birds in a cage. A birth and death chain5.8 Trees in a forest. An absorbing birth and death chain; Exercises; 6 Stationary distributions; 6.1 The certainty of death; 6.2 Elevator stationarity. The stationary birth and death process; 6.3 How long is the queue at the checkout? A first look; 6.4 How long is the queue at the checkout? A second look; 6.5 How long must someone wait at the checkout? Another view; 6.6 The structure of the work force; 6.7 When does a T-junction require a left-turn lane?; Exercises; 7 Optimal decision and reward; 7.1 How much should a buyer buy? A first look ; 7.2 How many roses for Valentine's Day?
• Sommario/riassunto: WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "" . . . [a] treasure house of material for students and teachers alike . . . can be dipped into regularly for inspiration and ideas. It deserves to become a classic.""-London Times Highe
• Titolo autorizzato: Concrete approach to mathematical modelling
• ISBN: 1-282-25159-7; 9786613813893; 1-118-03248-9; 1-118-03064-8
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910877090703321
• Lo trovi qui: Univ. Federico II