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Mathematical Modelling
- 1st Edition
- Authors: D.N.P. Murthy, E.Y. Rodin, N.W. Page
- Language: English
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… Read more
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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.
For senior undergraduates and postgraduates in engineering, physical, biological and social sciences, and mathematics.
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.
- Language: English
- Edition: 1
- Published:
- Imprint: Pergamon
ER
E.Y. Rodin
Affiliations and expertise
Department of Systems Science and Applied Mathematics, Washington University, USANP
N.W. Page
Affiliations and expertise
Department of Mechanical Engineering, University of Queensland, Australia