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 Problemssformations 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 Problemstegral Transforms The Method of Characteristics Practice Problems.