This text demonstrates the process of comprehensive applied mathematical modeling through the introduction of various case studies. The case studies are arranged in increasing order of complexity based on the mathematical methods required to analyze the models. The development of these methods is also included, providing a self-contained presentation. To reinforce and supplement the material introduced, original problem sets are offered involving case studies closely related to the ones presented. With this style, the text’s perspective, scope, and completeness of the subject matter are considered unique. Having grown out of four self-contained courses taught by the authors, this text will be of use in a two-semester sequence for advanced undergraduate and beginning graduate students, requiring rudimentary knowledge of advanced calculus and differential equations, along with a basic understanding of some simple physical and biological scientific principles.

Presents a thorough grounding in the techniques of mathematical modelling, and proceeds to explore a range of classical and continuum models from an array of disciplines.

This is a book about the nature of mathematical modeling, and about the kinds of techniques that are useful for modeling. The text is in four sections. The first covers exact and approximate analytical techniques; the second, numerical methods; the third, model inference based on observations; and the last, the special role of time in modeling. Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area. The text is complemented by extensive worked problems.

This book addresses the construction, analysis, and intepretation of mathematical models that shed light on significant problems in the physical sciences, with exercises that reinforce, test and extend the reader's understanding. It may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers.

Pulling Rabbits Out of Hats: Using Mathematical Modeling in the Material, Biophysical, Fluid Mechanical, and Chemical Sciences focuses on those assumptions made during applied mathematical modeling in which the phenomenological data and the model predictions are self-consistent. This comprehensive reference demonstrates how to employ a variety of mathematical techniques to quantify a number of problems from the material, biophysical, fluid mechanical, and chemical sciences. In doing so, methodology of modelling, analysis, and result generation are all covered. Key Features: Includes examples on such cases as solidification of alloys, chemically-driven convection of dissociating gases, temperature-dependent predator-prey mite systems, multi-layer and two-phase fluid phenomena, viral-target cell interactions, diffusive and gravitational instabilities, and chemical, material science, optical, and ecological Turing patterns. Aims to make the process of quantification of scientific phenomena transparent. Is a hybrid semi-autobiographical account of research results and a monograph on pattern formation. This book is for everyone with an interest in how both scientific contributions are made and mathematical modelling is developed from first principles in STEM fields. For errata, please visit the author's website.

Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.

Research efforts in the past ten years have led to considerable advances in the concepts and methods of smart manufacturing. Smart Manufacturing: Concepts and Methods puts these advances in perspective, showing how process industries can benefit from these new techniques. The book consolidates results developed by leading academic and industrial groups in the area, providing a systematic, comprehensive coverage of conceptual and methodological advances made to date. Written by leaders in the field from around the world, Smart Manufacturing: Concepts and Methods is essential reading for graduate students, researchers, process engineers, and managers. It is complemented by a companion book titled Smart Manufacturing: Applications and Case Studies, which covers the applications of smart manufacturing concepts and methods in process industries and beyond. - Takes a process-systems engineering approach to design, monitoring, and control of smart manufacturing systems - Brings together the key concepts and methods of smart manufacturing, including the advances made in the past decade - Includes coverage of computation methods for process optimization, control, and safety, as well as advanced modelling techniques