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.