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Thoroughly revised and updated, The Art of Modeling in Science and Engineering with Mathematica®, Second Edition explores the mathematical tools and procedures used in modeling based on the laws of conservation of mass, energy, momentum, and electrical charge. The authors have culled and consolidated the best from the first edition and expanded the range of applied examples to reach a wider audience. The text proceeds, in measured steps, from simple models of real-world problems at the algebraic and ordinary differential equations (ODE) levels to more sophisticated models requiring partial differential equations. The traditional solution methods are supplemented with Mathematica , which is used throughout the text to arrive at solutions for many of the problems presented. The text is enlivened with a host of illustrations and practice problems drawn from classical and contemporary sources. They range from Thomson’s famous experiment to determine e/m and Euler’s model for the buckling of a strut to an analysis of the propagation of emissions and the performance of wind turbines. The mathematical tools required are first explained in separate chapters and then carried along throughout the text to solve and analyze the models. Commentaries at the end of each illustration draw attention to the pitfalls to be avoided and, perhaps most important, alert the reader to unexpected results that defy conventional wisdom. These features and more make the book the perfect tool for resolving three common difficulties: the proper choice of model, the absence of precise solutions, and the need to make suitable simplifying assumptions and approximations. The book covers a wide range of physical processes and phenomena drawn from various disciplines and clearly illuminates the link between the physical system being modeled and the mathematical expression that results.
Modeling is practiced in engineering and all physical sciences. Many specialized texts exist - written at a high level - that cover this subject. However, students and even professionals often experience difficulties in setting up and solving even the simplest of models. This can be attributed to three difficulties: the proper choice of model, the absence of precise solutions, and the necessity to make suitable simplifying assumptions and approximations. Overcoming these difficulties is the focus of The Art of Modeling in Science and Engineering. The text is designed for advanced undergraduate and graduate students and practicing professionals in the sciences and engineering with an interest in Modeling based on Mass, Energy and Momentum or Force Balances. The book covers a wide range of physical processes and phenomena drawn from chemical, mechanical, civil, environmental sciences and bio- sciences. A separate section is devoted to "real World" industrial problems. The author explains how to choose the simplest model, obtain an appropriate solution to the problem and make simplifying assumptions/approximations.
This instructor's manual is designed to accompany Mathematical Modeling of Physical Systems, as a supplement to Diran Basmadjian's main text. It contains solutions to all the practice problems.
Since the 4th 1998 edition, there have been numerous crucial advances to the modelling and the basic understanding of solidification phenomena, and with its linking to experimental results. These topics have been incorporated into this 5th Fully Revised Edition, as well as a new final chapter on microstructure selection which explains how to combine the concepts of the preceding chapters for modelling real microstructures, in complex processes such as additive manufacturing. This new 5th edition is of high interest to undergraduate and graduate levels and professionals. With its numerous new topics - also borne out by the new authorship - students and teachers, scientists and engineers will greatly benefit from this new book. The topics are presented in the same praised manner as in previous editions, readable at three levels: - an initial feel for the subject is obtained by consulting the figures and their detailed captions; - a deeper understanding of the underlying physics is found by working through the main text; - 15 appendices offer a detailed analysis of the various theories, by providing detailed derivations of the relevant equations. Particularly Novel: the final chapter 8 on microstructure-selection explains how to combine the concepts of the preceding chapters to model the real microstructures formed during complex processes such as additive manufacturing, and the new detailed phase-field appendix which opens the door to the accurate computer-modelling of growth-forms. This edition goes with a companion Solutions Manual offering model solutions to 133 problems (exercises).
Now in its fourth edition, Powell and Baker’s Management Science: The Art of Modeling with Spreadsheets, 4th Edition provides students and business analysts with the technical knowledge and skill needed to develop real expertise in business modeling. In this book, the authors cover spreadsheet engineering, management science, and the modeling craft. Management Science, 4th Edition provides students and business analysts with the technical knowledge and skill needed to develop real expertise in business modeling. The authors cover spreadsheet engineering, management science, and the modeling craft. The text is designed to improve modeling efficiency and modeling effectiveness by focusing on the most important tasks and tools.
A powerful, unified approach to mathematical and computational modeling in science and engineering Mathematical and computational modeling makes it possible to predict the behavior of a broad range of systems across a broad range of disciplines. This text guides students and professionals through the axiomatic approach, a powerful method that will enable them to easily master the principle types of mathematical and computational models used in engineering and science. Readers will discover that this axiomatic approach not only enables them to systematically construct effective models, it also enables them to apply these models to any macroscopic physical system. Mathematical Modeling in Science and Engineering focuses on models in which the processes to be modeled are expressed as systems of partial differential equations. It begins with an introductory discussion of the axiomatic formulation of basic models, setting the foundation for further topics such as: Mechanics of classical and non-classical continuous systems Solute transport by a free fluid Flow of a fluid in a porous medium Multiphase systems Enhanced oil recovery Fluid mechanics Throughout the text, diagrams are provided to help readers visualize and better understand complex mathematical concepts. A set of exercises at the end of each chapter enables readers to put their new modeling skills into practice. There is also a bibliography in each chapter to facilitate further investigation of individual topics. Mathematical Modeling in Science and Engineering is ideal for both students and professionals across the many disciplines of science and engineering that depend on mathematical and computational modeling to predict and understand complex systems.