This book explores the mathematical tools and procedures used in modeling based on the laws of conservation of mass, energy, momentum, and electrical charge. This edition expands the range of applied examples to reach a wider audience. The text proceeds 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.
A First Look at Modeling | Analytical Tools: The Solution of Ordinary Differential Equations | The Use of Mathematica
in Modeling Physical Systems | Elementary Applications of the Conservation Laws | Partial Differential Equations: Classification, Types, and Properties--Some Simple Transformations | Solution of Linear Systems by Superposition Methods | Vector Calculus: Generalized Transportation Equations | Analytical Solutions of Partial Differential Equations