The Art of Modeling in Science and Engineering with Mathematica: 2nd Edition (Hardback) book cover

The Art of Modeling in Science and Engineering with Mathematica

2nd Edition

By Diran Basmadjian, Ramin Farnood

Chapman and Hall/CRC

509 pages | 100 B/W Illus.

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pub: 2006-08-18
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Description

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

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT021000
MATHEMATICS / Number Systems