Matrix, Numerical, and Optimization Methods in Science and Engineering
Cambridge University Press, 3/4/2021
EAN 9781108479097, ISBN10: 110847909X
Hardcover, 600 pages, 25.4 x 17.8 x 4.4 cm
Language: English
Originally published in English
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.
Part I. Matrix Methods
1. Vector and matrix algebra
2. Algebraic eigenproblems and their applications
3. Differential eigenproblems and their applications
4. Vector and matrix calculus
5. Analysis of discrete dynamical systems
Part II. Numerical Methods
6. Computational linear algebra
7. Numerical methods for differential equations
8. Finite-difference methods for boundary-value problems
9. Finite-difference methods for initial-value problems
Part III. Least Squares and Optimization
10. Least-squares methods
11. Data analysis – curve fitting and interpolation
12. Optimization and root finding of algebraic systems
13. Data-driven methods and reduced-order modeling.