The Art of Modeling in Science and Engineering with Mathematica. (2006)

• Record Type: Book
• Further Information: Note: Diran Basmadjian, Ramin Farnood.
• Authors: Basmadjian, Diran; Farnood, Ramin
• 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
• Edition: Second edition
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2006
• Extent: 1 online resource
• Subjects: 501.5118; Mathematical models; Numerical analysis; Mathematical physics; Mechanics, Applied; Mathematical models; Mathematical physics; Mechanics, Applied; Numerical analysis; Electronic books
• Languages: English
• ISBNs: 9781482286038; 1482286033
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.