The Art of Modeling in Science and Engineering with Mathematica, Second Edition / Diran Basmadjian, Ramin Farnood.

Author
Basmadjian, Diran [Browse]
Format
Book
Language
English
Εdition
Second edition.
Published/​Created
Boca Raton, FL : CRC Press, 2006.
Description
1 online resource : text file, PDF

Availability

Details

Subject(s)
Author
Summary note
"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 Thomsons famous experiment to determine e/m and Eulers 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."--Provided by publisher.
Contents
  • Cover; Half Title; Title Page; Copyright Page; Preface to Second Edition; Abstract; Biographies; Table of Contents; Chapter 1: A First Look at Modeling; 1.1 The Physical Laws; 1.1.1 Conservation Laws; 1.1.2 Auxiliary Relations; 1.1.3 The Balance Space and Its Geometry; 1.2 The Rate of the Variables: Dependent and Independent Variables; 1.3 The Role of Balance Space: Differential and Integral Balances; 1.4 The Role of Time: Unsteady State and Steady State Balances; 1.5 Information Derived from Model Solutions; 1.6 Choosing a Model; 1.7 Kick-Starting the Modeling Process; 1.8 Solution Analysis
  • Practice ProblemsChapter 2: Analytical Tools: The Solution of Ordinary Differential Equations; 2.1 Definitions and Classifications; 2.1.1 Order of an ODE; 2.1.2 Linear and Nonlinear ODEs; 2.1.3 ODEs with Variable Coefficients; 2.1.4 Homogeneous and Nonhomogeneous ODEs; 2.1.5 Autonomous ODEs; 2.2 Boundary and Initial Conditions; 2.2.1 Some Useful Hints on Boundary Conditions; 2.3 Analytical Solutions of ODEs; 2.3.1 Separation of Variables; 2.3.2 The D-Operator Method. Solution of Linear n-th-Order ODEs with Constant Coefficients
  • 2.3.3 Nonhomogeneous Linear Second-Order ODEs with Constant Coefficients2.3.4 Series Solutions of Linear ODEs with Variable Coefficients; 2.3.5 Other Methods; 2.4 Nonlinear Analysis; 2.4.1 Phase Plane Analysis: Critical Points; 2.5 Laplace Transformation; 2.5.1 General Properties of the Laplace Transform; 2.5.2 Application to Differential Equations; Practice Problems; Chapter 3: The Use of Mathematica in Modeling Physical Systems; 3.1 Handling Algebraic Expressions; 3.2 Algebraic Equations; 3.2.1 Analytical Solution to Algebraic Equations; 3.2.2 Numerical Solution to Algebraic Equations
  • 3.3 Integration3.4 Ordinary Differential Equations; 3.4.1 Analytical Solution to ODEs; 3.4.2 Numerical Solution to Ordinary Differential Equation; 3.5 Partial Differential Equations; Practice Problems; Chapter 4: Elementary Applications of the Conservation Laws; 4.1 Application of Force Balances; 4.2 Applications of Mass Balances; 4.2.1 Compartmental Models; 4.2.2 Distributed Systems; 4.3 Applications of Energy Balances; 4.3.1 Compartmental Models; 4.3.2 Distributed Models; 4.4 Simultaneous Applications of the Conservation Laws; Practice Problems
  • Chapter 5: Partial Differential Equations: Classification, Types, and Properties
  • Some Simple Transformations5.1 Properties and Classes of PDEs; 5.1.1 Order of a PDE; 5.1.1.1 First-Order PDEs; 5.1.1.2 Second-Order PDEs; 5.1.1.3 Higher-Order PDEs; 5.1.2 Homogeneous PDEs and BCs; 5.1.3 PDEs with Variable Coefficients; 5.1.4 Linear and Nonlinear PDEs: A New Category
  • Quasilinear PDEs; 5.1.5 Another New Category: Elliptic, Parabolic, and Hyperbolic PDEs; 5.1.6 Boundary and Initial Conditions; 5.2 PDEs of Major Importance; 5.2.1 First-Order Partial Differential Equations; 5.2.2 Second-Order PDEs
ISBN
  • 9781482286038 ((e-book))
  • 1482286033
OCLC
1027760587
Statement on language in description
Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage. Read more...
Other views
Staff view