Cassel K.W. Matrix, Numerical, and Optimization Methods in Science and Engineering

Cambridge: Cambridge University Press, 2021. — 727 p. — ISBN 9781108782333.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.Matrix Methods
Vector and Matrix Algebra
Algebraic Eigenproblems and Their Applications
Differential Eigenproblems and Their Applications
Vector and Matrix Calculus
Analysis of Discrete Dynamical Systems
Numerical Methods
Computational Linear Algebra
Numerical Methods for Differential Equations
Finite-Difference Methods for Boundary-Value Problems
Finite-Difference Methods for Initial-Value Problems
Least Squares and Optimization
Least-Squares Methods
Data Analysis: Curve Fitting and Interpolation
Optimization and Root Finding of Algebraic Systems
Data-Driven Methods and Reduced-Order Modeling