Foundations of Mathematical Modeling and Analysis for Engineering is designed for first-year graduate and advanced undergraduate engineering students. The book explores linear system theory and demonstrates its application in developing analytical solutions to various equations, essential for describing physical systems through mathematical modeling. This foundation is crucial for learning and research in engineering and various scientific fields. It equips students with the mathematical tools needed to solve entire classes of linear algebraic, ordinary-, and partial-differential equations, while also teaching principles for formulating, organizing, and solving linear subsystems, all of which are vital components of both linear and nonlinear mathematical models. This knowledge prepares students for advanced studies in engineering, applied mathematics, and foundational sciences.