09-23-2026, 08:51 PM
Mathematical Models and Their Analysis by Frederic Y. M. Wan is a textbook on how mathematics can be used to formulate, analyze, and interpret models of real-world phenomena. Rather than treating mathematical techniques in isolation, it introduces them through concrete problems from physics, engineering, traffic, environmental management, economics, and resource allocation. The book develops tools including dimensional analysis, ordinary and partial differential equations, perturbation methods, stability analysis, eigenvalue problems, calculus of variations, optimization, and optimal control.
A central theme is that mathematical modeling is an iterative process: begin with a simplified but meaningful model, analyze its behavior, compare its predictions with observations, and refine it when necessary. The applications range from Kepler's planetary laws, Mercury's orbital precession, elastic buckling, traffic flow, shallow-water waves, and heat conduction to fishing limits, urban development, economic growth, renewable resources, and forest harvesting. The final appendix introduces controllability of linear systems, extending the book toward control theory.
Overall, it emphasizes how the same mathematical structures—especially differential equations and optimization—can illuminate very different real-world problems.
BOOK
A central theme is that mathematical modeling is an iterative process: begin with a simplified but meaningful model, analyze its behavior, compare its predictions with observations, and refine it when necessary. The applications range from Kepler's planetary laws, Mercury's orbital precession, elastic buckling, traffic flow, shallow-water waves, and heat conduction to fishing limits, urban development, economic growth, renewable resources, and forest harvesting. The final appendix introduces controllability of linear systems, extending the book toward control theory.
Overall, it emphasizes how the same mathematical structures—especially differential equations and optimization—can illuminate very different real-world problems.
BOOK
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