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Numerical Methods for Large Eigenvalue Problems

Author : Yousef Saad

Publisher : SIAM

Page : 292 pages

File Size : 41,53 MB

Release : 2011-01-01

Category : Mathematics

ISBN : 9781611970739

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Book Description

This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.



Eigenfunctions of the Laplacian on a Riemannian Manifold

Author : Steve Zelditch

Publisher : American Mathematical Soc.

Page : 410 pages

File Size : 33,1 MB

Release : 2017-12-12

Category : Mathematics

ISBN : 1470410370

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Book Description

Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.





Feedback Systems

Author : Karl Johan Åström

Publisher : Princeton University Press

Page : pages

File Size : 21,63 MB

Release : 2021-02-02

Category : Technology & Engineering

ISBN : 069121347X

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Book Description

The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory



Chebyshev and Fourier Spectral Methods

Author : John P. Boyd

Publisher : Courier Corporation

Page : 690 pages

File Size : 43,13 MB

Release : 2001-12-03

Category : Mathematics

ISBN : 0486411834

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Book Description

Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.



Quantum Mechanics

Author : Leslie E. Ballentine

Publisher : World Scientific Publishing Company Incorporated

Page : 722 pages

File Size : 28,38 MB

Release : 2014-08-25

Category : Science

ISBN : 9789814578578

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Book Description

Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory.In this edition a new chapter on quantum information is added. As the topic is still in a state of rapid development, a comprehensive treatment is not feasible. The emphasis is on the fundamental principles and some key applications, including quantum cryptography, teleportation of states, and quantum computing. The impact of quantum information theory on the foundations of quantum mechanics is discussed. In addition, there are minor revisions to several chapters.The book is intended primarily as a graduate level textbook, but it will also be of interest to physicists and philosophers who study the foundations of QM. Parts of it can be used by senior undergraduates too.



Introduction to Random Graphs

Author : Alan Frieze

Publisher : Cambridge University Press

Page : 483 pages

File Size : 10,92 MB

Release : 2016

Category : Mathematics

ISBN : 1107118506

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Book Description

The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.



Nonlinear Dynamics and Chaos

Author : Steven H. Strogatz

Publisher : CRC Press

Page : 532 pages

File Size : 25,93 MB

Release : 2018-05-04

Category : Mathematics

ISBN : 0429961111

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Book Description

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.



An Introductory Course of Particle Physics

Author : Palash B. Pal

Publisher : Taylor & Francis

Page : 818 pages

File Size : 17,11 MB

Release : 2014-07-29

Category : Science

ISBN : 1482216981

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Book Description

For graduate students unfamiliar with particle physics, An Introductory Course of Particle Physics teaches the basic techniques and fundamental theories related to the subject. It gives students the competence to work out various properties of fundamental particles, such as scattering cross-section and lifetime. The book also gives a lucid summary of the main ideas involved. In giving students a taste of fundamental interactions among elementary particles, the author does not assume any prior knowledge of quantum field theory. He presents a brief introduction that supplies students with the necessary tools without seriously getting into the nitty-gritty of quantum field theory, and then explores advanced topics in detail. The book then discusses group theory, and in this case the author assumes that students are familiar with the basic definitions and properties of a group, and even SU(2) and its representations. With this foundation established, he goes on to discuss representations of continuous groups bigger than SU(2) in detail. The material is presented at a level that M.Sc. and Ph.D. students can understand, with exercises throughout the text at points at which performing the exercises would be most beneficial. Anyone teaching a one-semester course will probably have to choose from the topics covered, because this text also contains advanced material that might not be covered within a semester due to lack of time. Thus it provides the teaching tool with the flexibility to customize the course to suit your needs.



Numerical Recipes in C++

Author : William H. Press

Publisher :

Page : 0 pages

File Size : 41,75 MB

Release : 2002

Category : Computers

ISBN : 9788175960961

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Book Description

Now the acclaimed Second Edition of Numerical Recipes is available in the C++ object-oriented programming language. Including and updating the full mathematical and explanatory contents of Numerical Recipes in C, this new version incorporates completely new C++ versions of the more than 300 Numerical Recipes routines that are widely recognized as the most accessible and practical basis for scientific computing. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. Highlights include linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations and inverse theory. The authors approach to C++ preserves the efficient execution that C users expect, while simultaneously employing a clear, object-oriented interface to the routines. Tricks and tips for scientific computing in C++ are liberally included. The routines, in ANSI/ISO C++ source code, can thus be used with almost any existing C++ vector/matrix class library, according to user preference. A simple class library for stand-alone use is also included in the book. Both scientific programmers new to C++, and experienced C++ programmers who need access to the Numerical Recipes routines, can benefit from this important new version of an invaluable, classic text.