This practical, applications-oriented text demonstrates the key role of mathematics in optimization and linear systems. It explains effective procedures for performing mathematical tasks that arise in many fields, including operations research, engineering, systems sciences, statistics, and economics. Readers will learn how to resolve linear independence and find null spaces and factors of matrices, determine existence of restricted solutions to linear equations and inequalities, and resolve definiteness of Hermitian and real symmetric matrices by Gaussian pivoting. Additional topics include how to diagonalize — or "nearly" diagonalize — square matrices, differentiate vectors and matrices by the chain rule, solve systems of differential and difference equations, and other subjects. Most of the examples and many of the 1,300 problems illustrate techniques, and nearly all of the tables display reference material for procedures. Differential and integral calculus are prerequisites.