Matrix, Numerical, and Optimization Methods in Science and Engineering

Address vector and matrix methods necessary in numerical methods and optimization of linear systems with this practical text.

Kevin W. Cassel (Author)

9781108479097, Cambridge University Press

Hardback, published 4 March 2021

600 pages
23 x 15 x 4.5 cm, 1.39 kg

'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

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.

Subject Areas: Mathematical theory of computation [UYA], Maths for engineers [TBJ], Dynamics & statics [PHDT], Fluid mechanics [PHDF], Optimization [PBU], Numerical analysis [PBKS], Calculus & mathematical analysis [PBK]