Address vector and matrix methods necessary in numerical methods and optimization of linear systems in engineering with this unified text. Treats the mathematical models that describe and predict the evolution of our processes and systems, and the numerical methods required to obtain approximate solutions. Explores the dynamical systems theory used to describe and characterize system behaviour, alongside the techniques used to optimize their performance. Integrates and unifies matrix and eigenfunction methods with their applications in numerical and optimization methods. Consolidating, generalizing, and unifying these topics into a single coherent subject, this practical resource is suitable for advanced undergraduate students and graduate students in engineering, physical sciences, and applied mathematics.

'In this well-written reader friendly book, Professor Cassel systematically presents a wide range of mathematical concepts and methods, including matrix, numerical, and optimization methods, that are crucial in science and engineering. In particular, the book treats the mathematical models that describe and predict the evolution of various processes and systems, and the numerical methods required to obtain approximate solutions. It also explores the dynamical systems theory used to describe and characterize system behavior, alongside the techniques used to optimize their performance. The book integrates and unifies matrix and eigenfunction methods with their applications in numerical and optimization methods. This book is a valuable reference or textbook for advanced undergraduate and graduate students in engineering, physical sciences, and applied mathematics.'

Zhongshan Li - Georgia State University

'The book offers an attractive and innovative approach to integrating matrix and numerical methods with optimization techniques in the context of dynamical systems. It would serve well as a text in a course for advanced undergraduates and graduate students in science and engineering.'

Bill Saltzer Ph.D. - Retired, Applied Mathematician, 3M

'This text strikes just the right balance between mathematical rigor and applications for engineers and mathematical scientists. Numerous applications show the natural connection between discreet and continuous models and their mathematical counterparts-matrix methods and differential equations.'

Joel A. Storch - California State University, Northridge

The author has used a brilliant approach to engage his audience of engineers and scientists by tapping their curiosity about applications, then motivating them through explanation and finally applying the concepts learned right away. This book can serve as an excellent standard text for applied mathematics, with each chapter formally presented according to the pattern "motivate→learn→interpret→apply→extend ... Highly recommended.'

M. O. Farooq Source: Choice