Foundations of Mathematical Modeling and Analysis in Engineering
- 1st Edition - December 11, 2025
- Latest edition
- Author: A. Ted Watson
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 2 9 5 9 2 - 8
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 2 9 5 9 3 - 5
Foundations of Mathematical Modeling and Analysis for Engineering is designed for first-year graduate and advanced undergraduate engineering students. The book explores linear sy… Read more
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.
- Serves as an extensive toolbox for graduate engineering students, covering both foundational and complex mathematical concepts essential for advanced studies
- Emphasizes real-world applications of mathematical models, bolstering problem-solving skills through worked examples and end-of-chapter exercises
- Aids the transition from undergraduate to graduate studies, ensuring comprehensive understanding and application of the mathematical concepts in advanced engineering coursework
First-year graduate engineering students across all engineering disciplines.
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
Appendices
A. A Word on Proofs
B. Vector calculus and operations
C. Simulate measurement errors
D. Additional operations with square matrices
E. Addendum to Chapter 7
F. Higher-Order Linear ODEs
G. QR Factorization
H. Sequences and Convergence
I. Eulers Equidimensional Equation
J. Sturm-Liouville Equations
K. Bessel’s equation
L. Best linear unbiased predictions and estimates
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
Appendices
A. A Word on Proofs
B. Vector calculus and operations
C. Simulate measurement errors
D. Additional operations with square matrices
E. Addendum to Chapter 7
F. Higher-Order Linear ODEs
G. QR Factorization
H. Sequences and Convergence
I. Eulers Equidimensional Equation
J. Sturm-Liouville Equations
K. Bessel’s equation
L. Best linear unbiased predictions and estimates
- Edition: 1
- Latest edition
- Published: December 11, 2025
- Language: English
AW
A. Ted Watson
Professor Watson holds a BS from the 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) and is now at Colorado State University (CSU), which he joined as founding department head of chemical & biological engineering. Throughout his career, he has developed methods for mathematical modeling and system and parameter identification, working with important systems ranging from quantum to geological scales. He established and directed the Engineering Imaging Laboratory at TAMU and Rocky Mountain Magnetic Resonance at CSU and was recently elected Fellow of the American Institute of Chemical Engineers (AIChE).
Affiliations and expertise
Department of Chemical and Biological Engineering, Colorado State University, Fort Collins, CO, USA