Ebook: Mathematical Modelling: Concepts and Case Studies

Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science and engineering. There has been a constant movement in the emphasis from developing proficiency in purely mathematical techniques to an approach which caters for industrial and scientific applications in emerging new technologies. In this textbook we have attempted to present the important fundamental concepts of mathematical modelling and to demonstrate their use in solving certain scientific and engineering problems. This text, which serves as a general introduction to the area of mathematical modelling, is aimed at advanced undergraduate students in mathematics or closely related disciplines, e.g., students who have some prerequisite knowledge such as one-variable calculus, linear algebra and ordinary differential equations. Some prior knowledge of computer programming would be useful but is not considered essential. The text also contains some more challenging material which could prove attractive to graduate students in engineering or science who are involved in mathematical modelling. In preparing the text we have tried to use our experience of teaching mathematical modelling to undergraduate students in a wide range of areas including mathematics and computer science and disciplines in engineering and science. An important aspect of the text is the use made of scientific computer software packages such as MAPLE for symbolic algebraic manipulations and MA TLAB for numerical simulation.

---

This book serves as a general introduction to the area of mathematical modelling. It attempts to present the important fundamental concepts of mathematical modelling and to demonstrate their use in solving certain scientific and engineering problems.
The book has the advantage that it deals with both modelling concepts and case studies. Part I considers continuous and discrete modelling while Part II consists of a number of realistic case studies which illustrate the use of the modelling process in the solution of continuous and discrete models.
Audience: The text is aimed at advanced undergraduate students and graduates in mathematics or closely related engineering and science disciplines, e.g. students who have some prerequisite knowledge such as one-variable calculus, linear algebra and ordinary differential equations.

---

This book serves as a general introduction to the area of mathematical modelling. It attempts to present the important fundamental concepts of mathematical modelling and to demonstrate their use in solving certain scientific and engineering problems.
The book has the advantage that it deals with both modelling concepts and case studies. Part I considers continuous and discrete modelling while Part II consists of a number of realistic case studies which illustrate the use of the modelling process in the solution of continuous and discrete models.
Audience: The text is aimed at advanced undergraduate students and graduates in mathematics or closely related engineering and science disciplines, e.g. students who have some prerequisite knowledge such as one-variable calculus, linear algebra and ordinary differential equations.
Content:
Front Matter....Pages I-XII
Front Matter....Pages 1-1
Formulation of Mathematical Models....Pages 3-32
Compartment Problems....Pages 33-65
Models in Dynamics and Vibration....Pages 67-141
Discrete Models....Pages 143-173
Numerical Techniques for Model Nonlinear PDE’s....Pages 175-199
Front Matter....Pages 201-201
The Design of Biotreatment Systems....Pages 203-226
Dynamics of Contagious Disease....Pages 227-242
Numerical Cam Design....Pages 243-260
Dynamics and Force Analysis of a Mechanism....Pages 261-280
Back Matter....Pages 281-287

---

This book serves as a general introduction to the area of mathematical modelling. It attempts to present the important fundamental concepts of mathematical modelling and to demonstrate their use in solving certain scientific and engineering problems.
The book has the advantage that it deals with both modelling concepts and case studies. Part I considers continuous and discrete modelling while Part II consists of a number of realistic case studies which illustrate the use of the modelling process in the solution of continuous and discrete models.
Audience: The text is aimed at advanced undergraduate students and graduates in mathematics or closely related engineering and science disciplines, e.g. students who have some prerequisite knowledge such as one-variable calculus, linear algebra and ordinary differential equations.
Content:
Front Matter....Pages I-XII
Front Matter....Pages 1-1
Formulation of Mathematical Models....Pages 3-32
Compartment Problems....Pages 33-65
Models in Dynamics and Vibration....Pages 67-141
Discrete Models....Pages 143-173
Numerical Techniques for Model Nonlinear PDE’s....Pages 175-199
Front Matter....Pages 201-201
The Design of Biotreatment Systems....Pages 203-226
Dynamics of Contagious Disease....Pages 227-242
Numerical Cam Design....Pages 243-260
Dynamics and Force Analysis of a Mechanism....Pages 261-280
Back Matter....Pages 281-287
....