Modeling is practiced in engineering and all physical sciences. Many specialized texts exist - written at a high level - that cover this subject. However, students and even professionals often experience difficulties in setting up and solving even the simplest of models. This can be attributed to three difficulties: the proper choice of model, the absence of precise solutions, and the necessity to make suitable simplifying assumptions and approximations. Overcoming these difficulties is the focus of The Art of Modeling in Science and Engineering. The text is designed for advanced undergraduate and graduate students and practicing professionals in the sciences and engineering with an interest in Modeling based on Mass, Energy and Momentum or Force Balances. The book covers a wide range of physical processes and phenomena drawn from chemical, mechanical, civil, environmental sciences and bio- sciences. A separate section is devoted to "real World" industrial problems. The author explains how to choose the simplest model, obtain an appropriate solution to the problem and make simplifying assumptions/approximations.

Contenuti

INTRODUCTION
Conservation Laws and Auxiliary Relations
Properties and Categories of Balances
Three Physical Configurations
Types of ODE and AE Mass Balance
Information Obtained from Model Solutions
THE SETTING UP OF BALANCES
MORE ABOUT MASS, ENERGY AND MOMENTUM BALANCES
The Terms in Various Balances
Mass Balances
Energy Balances
Force and Momentum Balances
Combined Mass and Energy Balances
Combined Mass, Energy and Momentum Balances
ORDINARY DIFFERENTIAL EQUATIONS
Definitions and Classifications
Boundary and Initial Conditions
Analytical Solutions of ODEs
Numerical Methods
Non-Linear Analysis
THE LAPLACE TRANSFORMATION
General Properties of the Laplace Transform
Application to Differential Equations
Block Diagrams: A Simple Control System
Overall Transfer Function; Stability Criterion; Laplace Domain Analysis
SPECIAL TOPICS
Biomedical Engineering, Biology and Biotechnology
A Visit to the Environment
Welcome to the Real World
PARTIAL DIFFERENTIAL EQUATIONS: CLASSIFICATION, TYPES, AND PROPERTIES; SOME SIMPLE TRANSFORMATIONS AND SOLUTIONS
Properties and Classes of PDEs
PDEs of Major Importance
Useful Simplifications and Transformations
PDE's PDQ: Locating Solutions in Related Disciplines; Solution by Simple Superposition Methods
VECTOR CALCULUS: GENERALIZED TRANSPORT EQUATIONS
Vector Notation and Vector Calculus
Transport of Mass
Transport of Energy
Transport of Momentum
SOLUTION METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
Separation of Variables
Laplace Transformation and Other Integral Transforms
The Method of Characteristics

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