Mathematical modelling : a tool for problem solving in engineering, physical, biological, and social sciences
Author(s)
Bibliographic Information
Mathematical modelling : a tool for problem solving in engineering, physical, biological, and social sciences
（International series in modern applied mathematics and computer science, v. 20）
Pergamon Press, 1990
1st ed
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
The critical step in the use of mathematics for solving real world problems is the building of a suitable mathematical model. This book advocates a novel approach to the teaching of the building process for mathematical models, with emphasis on the art as well as the science aspects. Using a case study approach, the book teaches the mathematical modelling process in a comprehensive framework, presenting an overview of the concepts and techniques needed for modelling. The book is structured in three parts; the first dealing with the science aspect; the second dealing with the art aspects; and the third combining self learning exercises for the student and supplementary resource material for the instructor.
Table of Contents
Section headings and selected contents: Part I: Methodology and Tools: Role of Mathematics in Problem Solving. The nature of mathematical modelling. Problem Definition: The Starting Point. Case study E: World population. System Characterization. Static vs dynamic. Mathematical Modelling. Analog and simulation models. Mathematical Formulations - I. Partial differential equation (P.D.E) formulations. Analysis of Mathematical Formulations - I. Types of computers and the nature of computed solutions. Mathematical Formulations - II. Discrete state/continuous time formulations. Analysis of Mathematical Formulations - II. Analysis of stochastic processes. Simulation. Digital simulation methodology. Parameter Estimation. Stochastic model parameter estimation. Design of Experiment. Response surface design. Validation. Validation of stochastic models. Pitfalls in Modelling. Part II: Case Studies: Dynamics of Malaria Spread. System characterization. Designing a Pneumatic Pump. Forecasting Airline Passenger Growth. Part III: Supplementary Material: Modelling Exercises. Reference Material. Index.
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