The Art of Modeling in Science and Engineering with Mathematica

The Art of Modeling in Science and Engineering with Mathematica

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Thoroughly revised and updated, The Art of Modeling in Science and Engineering with Mathematica(R), 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 more

Product details

  • Hardback | 509 pages
  • 162 x 236 x 38mm | 879.98g
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 2nd Revised edition
  • 100 black & white illustrations
  • 1584884606
  • 9781584884606

Table of contents

A First Look at Modeling The Physical Laws The Rate of the Variables: Dependent and Independent Variables The Role of Balance Space: Differential and Integral Balances The Role of Time: Unsteady State and Steady State Balances Information Derived from Model Solutions Choosing a Model Kick-Starting the Modeling Process Solution Analysis Practice Problems Analytical Tools: The Solution of Ordinary Differential Equations Definitions and Classifications Boundary and Initial Conditions Analytical Solutions of ODEs Nonlinear Analysis Laplace Transformation Practice Problems The Use of Mathematica in Modeling Physical Systems Handling Algebraic Expressions Algebraic Equations Integration Ordinary Differential Equations Partial Differential Equations Practice Problems Elementary Applications of the Conservation Laws Application of Force Balances Applications of Mass Balance Simultaneous Applications of the Conservation Laws Practice Problems Partial Differential Equations: Classification, Types, and Properties - Some Simple Transformations Properties and Classes of PDE PDEs of Major Importance Useful Simplifications and Transformations PDEs PDQ: Locating Solutions in the Literature Practice Problems Solution of Linear Systems by Superposition Methods Superposition by Addition of Simple Flows: Solutions in Search of a Problem Superposition by Multiplication: Product Solutions Solution of Source Problems: Superposition by Integration More Superposition by Integration: Duhamel's Integral and the Superposition of Danckwerts Practice Problems Vector Calculus: Generalized Transport Equations Vector Notation and Vector Calculus Superposition Revisited: Green's Functions and the Solution of PDEs by Green's Functions Transport of Mass Transport of Energy Transport of Momentum Practice Problems Analytical Solutions of Partial Differential Equations Separation of Variables Laplace Transformation and Other Integral Transforms The Method of Characteristics Practice Problemsshow more