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Mathematical Modelling with Case Studies: A Differential Equations Approach using Maple and MATLAB, Second Edition (Textbooks in Mathematics) - Hardcover
Synopsis
Certain basic modeling skills can be applied to a wide variety of problems. It focuses on those mathematical techniques which are applicable to models involving differential equations. Models in three different areas are considered: growth and decay process, interacting populations and heating/cooling problems. The main mathematical technique is solving differential equations, while the range of applications and mathematical techniques presented provides a broad appreciation of this type of modeling. This book contains three general sections: Compartmental Models, Population Models and Heat Transfer Models. Within each section, the process of constructing a model is presented in full detail. Applications and case studies are integral to this text, and case studies are included throughout. This is a useful course text, and basic calculus and fundamental computing skills are required.
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Review
"The book is written in a very lucid manner, with numerous case studies and examples thoroughly discussed. The material is very well organized, generously illustrated, and delightfully presented. All chapters, except the first one, conclude with scores of nicely designed exercises that can be used for independent study. The book contains enough material to organize a new well-structured one-semester course or to complement the existing one with additional examples and problems and is highly recommended for either purpose"
―Zentralblatt MATH, 1168
"... The book can be useful for students of mathematical modeling. They will find many skills for modeling and solving real problems. Useful sheets for Maple and MATLAB are included for numerical solution. The most important feature of the book is that it contains many real-life examples. ... The main examples are solved in detail and the others are left for the reader. This is the best treasury of real case problems seen in a single book."
―EMS Newsletter, September 2009
From the Back Cover
Mathematical Modelling with Case Studies provides students with a firm grounding in basic modelling skills applicable to a wide variety of problems. The focus is on models involving differential equations, with the solution of differential equations as the primary technique used.The models considered relate to growth and decay processes, interacting populations, and heating/cooling problems, but the range of applications and mathematical techniques presented provide a broad appreciation of the scope of this type of modelling, while the skills developed readily transfer to many other areas.
Within each modelling section of the book, the authors carefully consider the procedure for constructing a model, emphasizing a start simple, evaluate, and then extend process. They use flow diagrams and word equations and discuss the assumptions made, consequent limitations, and impact on the interpretation of results--a structured, detailed approach that has proved a successful learning strategy. Along with theoretical and computational tools for analysis, the authors also encourage graphical methods and integrate throughout the text MAPLE code and its ensuing results.
The prerequisites for this text are minimal, including only a basic knowledge of calculus and fundamental computing skills. Thus the book is an excellent choice both for mathematics students and for those in the many other fields of study that require some expertise in modelling.
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