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Matrix, Numerical, and Optimization Methods in Science and Engineering [Hardback]

(Illinois Institute of Technology)
  • Formāts: Hardback, 600 pages, height x width x depth: 230x150x45 mm, weight: 1390 g, Worked examples or Exercises
  • Izdošanas datums: 04-Mar-2021
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 110847909X
  • ISBN-13: 9781108479097
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Matrix, Numerical, and Optimization Methods in Science and EngineeringPalielināt
  • Formāts: Hardback, 600 pages, height x width x depth: 230x150x45 mm, weight: 1390 g, Worked examples or Exercises
  • Izdošanas datums: 04-Mar-2021
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 110847909X
  • ISBN-13: 9781108479097
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781108479097.html
Keywords:
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.

Address vector and matrix methods necessary in numerical methods and optimization of linear systems with this practical, unified text. Perfect for advanced undergraduate students and graduate students in engineering, physical sciences, and applied mathematics.

Recenzijas

'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 "motivatelearninterpretapplyextend ... Highly recommended.' M. O. Farooq, Choice

Papildus informācija

Address vector and matrix methods necessary in numerical methods and optimization of linear systems with this practical text.
Preface xi
Part I Matrix Methods
1(312)
1 Vector and Matrix Algebra
3(61)
1.1 Introduction
5(5)
1.2 Definitions
10(3)
1.3 Algebraic Operations
13(2)
1.4 Systems of Linear Algebraic Equations -- Preliminaries
15(11)
1.5 Systems of Linear Algebraic Equations -- Solution Methods
26(11)
1.6 Vector Operations
37(5)
1.7 Vector Spaces, Bases, and Orthogonalization
42(9)
1.8 Linear Transformations
51(4)
1.9 Note on Norms
55(2)
1.10 Briefly on Bases
57(7)
Exercises
58(6)
2 Algebraic Eigenproblems and Their Applications
64(91)
2.1 Applications of Eigenproblems
64(5)
2.2 Eigenvalues and Eigenvectors
69(9)
2.3 Real Symmetric Matrices
78(13)
2.4 Normal and Orthogonal Matrices
91(4)
2.5 Diagonalization
95(5)
2.6 Systems of Ordinary Differential Equations
100(21)
2.7 Schur Decomposition
121(2)
2.8 Singular-Value Decomposition
123(12)
2.9 Polar Decomposition
135(3)
2.10 QR Decomposition
138(3)
2.11 Briefly on Bases
141(1)
2.12 Reader's Choice
141(14)
Exercises
142(13)
3 Differential Eigenproblems and Their Applications
155(63)
3.1 Function Spaces, Bases, and Orthogonalization
157(5)
3.2 Eigenfunctions of Differential Operators
162(17)
3.3 Adjoint and Self-Adjoint Differential Operators
179(10)
3.4 Partial Differential Equations -- Separation of Variables
189(20)
3.5 Briefly on Bases
209(9)
Exercises
210(8)
4 Vector and Matrix Calculus
218(35)
4.1 Vector Calculus
219(12)
4.2 Tensors
231(6)
4.3 Extrema of Functions and Optimization Preview
237(12)
4.4 Summary of Vector and Matrix Derivatives
249(1)
4.5 Briefly on Bases
250(3)
Exercises
250(3)
5 Analysis of Discrete Dynamical Systems
253(60)
5.1 Introduction
255(1)
5.2 Phase-Plane Analysis -- Linear Systems
256(4)
5.3 Bifurcation and Stability Theory -- Linear Systems
260(13)
5.4 Phase-Plane and Stability Analysis -- Nonlinear Systems
273(13)
5.5 Poincare and Bifurcation Diagrams -- Duffing Equation
286(13)
5.6 Attractors and Periodic Orbits -- Saltzman--Lorenz Model
299(14)
Part II Numerical Methods
313(214)
6 Computational Linear Algebra
315(61)
6.1 Introduction to Numerical Methods
317(9)
6.2 Approximation and Its Effects
326(8)
6.3 Systems of Linear Algebraic Equations -- Direct Methods
334(12)
6.4 Systems of Linear Algebraic Equations -- Iterative Methods
346(9)
6.5 Numerical Solution of the Algebraic Eigenproblem
355(16)
6.6 Epilogue
371(5)
Exercises
372(4)
7 Numerical Methods for Differential Equations
376(31)
7.1 General Considerations
377(7)
7.2 Formal Basis for Finite-Difference Methods
384(7)
7.3 Formal Basis for Spectral Numerical Methods
391(5)
7.4 Formal Basis for Finite-Element Methods
396(2)
7.5 Classification of Second-Order Partial Differential Equations
398(9)
Exercises
405(2)
8 Finite-Difference Methods for Boundary-Value Problems
407(59)
8.1 Illustrative Example from Heat Transfer
407(5)
8.2 General Second-Order Ordinary Differential Equation
412(3)
8.3 Partial Differential Equations
415(5)
8.4 Direct Methods for Linear Systems
420(6)
8.5 Iterative (Relaxation) Methods
426(4)
8.6 Boundary Conditions
430(4)
8.7 Alternating-Direction-Implicit (ADI) Method
434(3)
8.8 Multigrid Methods
437(7)
8.9 Compact Higher-Order Methods
444(4)
8.10 Treatment of Nonlinear Terms
448(18)
Exercises
453(13)
9 Finite-Difference Methods for Initial-Value Problems
466(61)
9.1 Introduction
466(1)
9.2 Single-Step Methods for Ordinary Differential Equations
467(14)
9.3 Additional Methods for Ordinary Differential Equations
481(2)
9.4 Partial Differential Equations
483(2)
9.5 Explicit Methods
485(4)
9.6 Numerical Stability Analysis
489(7)
9.7 Implicit Methods
496(5)
9.8 Boundary Conditions -- Special Cases
501(1)
9.9 Treatment of Nonlinear Convection Terms
502(6)
9.10 Multidimensional Problems
508(7)
9.11 Hyperbolic Partial Differential Equations
515(2)
9.12 Coupled Systems of Partial Differential Equations
517(1)
9.13 Parallel Computing
518(4)
9.14 Epilogue
522(5)
Exercises
522(5)
Part III Least Squares and Optimization
527(172)
10 Least-Squares Methods
529(31)
10.1 Introduction to Optimization
529(2)
10.2 Least-Squares Solutions of Algebraic Systems of Equations
531(7)
10.3 Least-Squares with Constraints
538(3)
10.4 Least-Squares with Penalty Functions
541(1)
10.5 Nonlinear Objective Functions
542(1)
10.6 Conjugate-Gradient Method
543(8)
10.7 Generalized Minimum Residual (GMRES) Method
551(4)
10.8 Summary of Krylov-Based Methods
555(5)
Exercises
556(4)
11 Data Analysis: Curve Fitting and Interpolation
560(34)
11.1 Linear Regression
560(8)
11.2 Polynomial Regression
568(2)
11.3 Least-Squares Regression as an Overdetermined System
570(2)
11.4 Least Squares with Orthogonal Basis Functions -- Fourier Series
572(6)
11.5 Polynomial Interpolation
578(1)
11.6 Spline Interpolation
579(2)
11.7 Curve Fitting and Interpolation of Multidimensional Data
581(3)
11.8 Linear Regression Using Singular-Value Decomposition
584(2)
11.9 Least-Squares Regression as State Estimation
586(3)
11.10 Definitions of the Residual
589(5)
Exercises
590(4)
12 Optimization and Root Finding of Algebraic Systems
594(48)
12.1 Introduction
594(1)
12.2 Nonlinear Algebraic Equations -- Root Finding
595(9)
12.3 Optimization
604(1)
12.4 Nonlinear Unconstrained Optimization
605(5)
12.5 Numerical Methods
610(5)
12.6 Nonlinear Constrained Optimization
615(5)
12.7 Linear Programming -- Formulation
620(7)
12.8 Linear Programming -- Simplex Method
627(7)
12.9 Optimal Control
634(8)
Exercises
637(5)
13 Data-Driven Methods and Reduced-Order Modeling
642(57)
13.1 Introduction
642(2)
13.2 Projection Methods for Continuous Systems
644(8)
13.3 Galerkin Projection and Reduced-Order Modeling for Continuous Systems
652(7)
13.4 Projection Methods for Discrete Systems
659(5)
13.5 Galerkin Projection and Reduced-Order Modeling for Discrete Systems
664(4)
13.6 Proper-Orthogonal Decomposition (POD) for Continuous Data
668(7)
13.7 Proper-Orthogonal Decomposition (POD) for Discrete Data
675(15)
13.8 Extensions and Alternatives to POD
690(6)
13.9 System Identification
696(1)
13.10 Epilogue
697(2)
References 699(4)
Index 703
Kevin W. Cassel is Professor of Mechanical and Aerospace Engineering and Professor of Applied Mathematics at the Illinois Institute of Technology. He is also an Associate Fellow of the American Institute of Aeronautics and Astronautics.