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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.
List of contents
1. Introduction
2. Mathematical representations of physical phenomena
3. Solving linear algebraic equations
4. Vector spaces and their representations
5. Linear transformations and representations
6. Inner product spaces
7. Operators and matrix representations
8. Ordinary differential equations
9. Function representation and transforms
10. Partial differential equations
11. System and parameter identification
About the author
Professor Emeritus A. Ted Watson holds a BS from University of Texas at Austin and a PhD from California Institute of Technology, both in chemical engineering. He attained the position of Professor at Texas A&M University (TAMU) before joining Colorado State University (CSU) as the founding department head of chemical & biological engineering. He has advanced mathematical modeling and system and parameter identification while working within a variety of fields. He established the Engineering Imaging Laboratory at TAMU and Rocky Mountain Magnetic Resonance at CSU and was elected Fellow of the American Institute of Chemical Engineers (AIChE).
