Foundations of Mathematical Modeling and Analysis for Engineering develops linear system theory at a level appropriate for first-year graduate and advanced undergraduate engineering students. It demonstrates the role of linear theory in developing analytical solutions to linear algebraic, ordinary-, and partial-differential equations, which provide the foundation for describing and advancing our understanding of physical systems through mathematical modeling. It provides the mathematics foundation for learning and research within engineering and many scientific disciplines.
This book provides the mathematical foundation for entry into graduate-level courses in engineering, applied mathematics, and any of the foundational sciences. Students will learn to determine all solutions to entire classes of linear algebraic, ordinary-, and partial-differential equations. They will learn principles for formulating, organizing, and solving linear subsystems that are important elements within linear and nonlinear mathematical models.
1. Mathematics and Engineering
2. Mathematical Models
3. Solving Linear Algebraic Equations
4. Vector Spaces and their Representations
5. Linear Transformations and Representations
6. Inner Product Spaces
7. Eigenvalues, Eigenvectors, and Canonical Forms
8. Ordinary Differential Equations
9. Function representations
10. Partial Differential Equations
11. System and Parameter Identification
Appendices
A. Notation
B. A word on proofs
C. Vector calculus and operations
D. Random variables
E. Additional operations with square matrices
F. Higher-order linear ODEs
G. QR factorization
H. Sequences and convergence
I. Euler’s equidimensional equation
J. Sturm-Liouville equations
K. Bessels equation
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