The Art of Modeling in Science and Engineering with Mathematica, Second Edition
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Summary
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.
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 Problems
Downloads Updates
| Resource | OS Platform | Updated | Description | Instructions |
|---|---|---|---|---|
| C4606.zip | Cross Platform | July 27, 2006 |
