数值分析导论（及答案） First published 2003

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中文名: 数值分析导论（及答案）

原名: An Introduction to Numerical Analysis & Solutions

作者: Endre Suli

David F. Mayers

图书分类: 科技

资源格式: PDF

版本: First published 2003

出版社: the press syndicate of the university of cambridge

书号: 0521810264

发行时间: 2003年

地区: 英国

语言: 英文

简介:

 

目录:

Preface page

1 Solution of equations by iteration 1

1.1 Introduction 1

1.2 Simple iteration 2

1.3 Iterative solution of equations 17

1.4 Relaxation and Newton’s method 19

1.5 The secant method 25

1.6 The bisection method 28

1.7 Global behaviour 29

1.8 Notes 32

Exercises 35

2 Solution of systems of linear equations 39

2.1 Introduction 39

2.2 Gaussian elimination 44

2.3 LU factorisation 48

2.4 Pivoting 52

2.5 Solution of systems of equations 55

2.6 Computational work 56

2.7 Norms and condition numbers 58

2.8 Hilbert matrix 72

2.9 Least squares method 74

2.10 Notes 79

Exercises 82

3 Special matrices 87

3.1 Introduction 87

3.2 Symmetric positive definite matrices 87

3.3 Tridiagonal and band matrices 93

7.6 The Euler–Maclaurin expansion 211

7.7 Extrapolation methods 215

7.8 Notes 219

Exercises 220

8 Polynomial approximation in the -norm 224

8.1 Introduction 224

8.2 Normed linear spaces 224

8.3 Best approximation in the -norm 228

8.4 Chebyshev polynomials 241

8.5 Interpolation 244

8.6 Notes 247

Exercises 248

9 Approximation in the 2-norm 252

9.1 Introduction 252

9.2 Inner product spaces 253

9.3 Best approximation in the 2-norm 256

9.4 Orthogonal polynomials 259

9.5 Comparisons 270

9.6 Notes 272

Exercises 273

10 Numerical integration – II 277

10.1 Introduction 277

10.2 Construction of Gauss quadrature rules 277

10.3 Direct construction 280

10.4 Error estimation for Gauss quadrature 282

10.5 Composite Gauss formulae 285

10.6 Radau and Lobatto quadrature 287

10.7 Note 288

Exercises 288

11 Piecewise polynomial approximation 292

11.1 Introduction 292

11.2 Linear interpolating splines 293

11.3 Basis functions for the linear spline 297

11.4 Cubic splines 298

11.5 Hermite cubic splines 300

11.6 Basis functions for cubic splines 302

11.7 Notes 306

Exercises 307

vi Contents

12 Initial value problems for ODEs 310

12.1 Introduction 310

12.2 One-step methods 317

12.3 Consistency and convergence 321

12.4 An implicit one-step method 324

12.5 Runge–Kutta methods 325

12.6 Linear multistep methods 329

12.7 Zero-stability 331

12.8 Consistency 337

12.9 Dahlquist’s theorems 340

12.10 Systems of equations 341

12.11 Stiff systems 343

12.12 Implicit Runge–Kutta methods 349

12.13 Notes 353

Exercises 355

13 Boundary value problems for ODEs 361

13.1 Introduction 361

13.2 A model problem 361

13.3 Error analysis 364

13.4 Boundary conditions involving a derivative 367

13.5 The general self-adjoint problem 370

13.6 The Sturm–Liouville eigenvalue problem 373

13.7 The shooting method 375

13.8 Notes 380

Exercises 381

14 The finite element method 385

14.1 Introduction: the model problem 385

14.2 Rayleigh–Ritz and Galerkin principles 388

14.3 Formulation of the finite element method 391

14.4 Error analysis of the finite element method 397

14.5 A posteriori error analysis by duality 403

14.6 Notes 412

Exercises 414

Appendix A An overview of results from real analysis 419

Appendix B WWW-resources 423

Bibliography 424

Index 429
内容介绍：

数值分析导论，牛津大学教材。最近好多难兄难弟在学数值分析，不忍看他们夜夜苦读，特此，翻出了尘封多年的这本书，以供参考。写的比其他版本简单很多，通俗易懂，没学过外语都能看懂的好东西。

作者介绍：

Endre S¨uli and David F. Mayers

应该是一对好基友，具体干什么的我也不知道，有兴趣的可以百度下。

算了，我百度了，大家看看吧。

David F. Mayer’s Overview

Current

Adjunct Professor at Monroe Community College

Partner at Harris Chesworth O’Brien

Past

Associate at HARRIS BEACH & WILCOX

Attorney at Winthrop Stimson

Attorney at Levinson & Passe

Education

Syracuse University College of Law

University of Wisconsin-Superior

Recommendations

4 people have recommended David F.

Connections

227 connections

Websites

Company Website

David F. Mayer’s Summary

Partner in General Practice Law Firm — Our firm offers comprehensive legal services in a wide variety of legal concerns in business, banking and finance, estate planning and administration, employment law, environmental matters, aspects of family law, litigation of all types, municipal affairs, real estate, taxation and finance planning. We are large enough to provide expertise in particular areas of law and small enough to provide personal attention from partners and associates to all clients. Our goal is to bring efficient, competent, professional service to you and assist you in successfully resolving your legal issues as quickly and inexpensively as possible.

Monroe Community College Faculty Adjunct Professor —

Department of Law and Criminal Justice, and

Paralegal Studies Program

Specialties

Law and Criminal Justice:

Fundamentals of New York Law;

Prisoner’s Rights

Paralegal Studies:

Wills and Estates;

Real Estate

Practice Focus:

Municipal Law;

Real Estate — Commerical and Residential;

Environmental;

Land Use;

Estates, Wills, Elder Law;

David F. Mayer’s Experience

Adjunct Professor

Monroe Community College

Educational Institution; 501-1000 employees; Higher Education industry

1996 – Present (16 years)

REAL PROPERTY LAW

Designed and taught paralegal certificate program course in Real Property Law. Train paraprofessional certificate candidates to handle real property transactions upon graduation, with sufficient understanding of legal theory to expand to more complex transactions. Document preparation, objective and subjective components, to master vocabulary and basic concepts, for real life scenarios.

BUSINESS ORGANIZATIONS/CORPORATE LAW

Designed and taught paralegal certificate program course in business organizations. A greater emphasis on use of State web sites and interaction with State agencies.

TRUSTS AND ESTATES LAW

Redesigned and taught paralegal certificate program course in Trusts and Estates. Train paraprofessional certificate candidates to handle estate planning and administration. Provide sufficient understanding of legal theory to enable graduates to grow in their field with experience.

LEGAL ASPECTS OF CORRECTIONS

Redesigned and taught course in laws affecting persons under supervision of criminal justice authorities. Emphasis on Civil Rights Act §1983, and Habeas Corpus. Explores state and Constitutional torts, and procedure of prisoner litigation in state and Federal courts. My redesign of the course involves in-depth examination of United States Supreme Court and Court of Appeals decisions, exploration of intersection of case law with practical day-to-day operation of correctional facilities, and tours of correctional facilities. Course is required for Corrections Majors.

INTRODUCTION TO THE LAW

Taught “Law 101”, an undergraduate survey course designed to introduce undergraduate students to a broad spectrum of legal matters, from the Bill of Rights to matrimonial and tort law. Provide real life information for typical citizen’s intersections with the law — from landlord tenant and credit issues to marriage/divorce and estates to contract requirements. Overview of the court structure and traffic/criminal law.

Partner

Harris Chesworth O’Brien

Partnership; 11-50 employees; Law Practice industry

June 1993 – Present (19 years 7 months)

I focus primarily on municipal law and legal concerns regarding property, including commerical and residential real estate, transfers in estates, wills and trusts, and environmental issues. My practice includes matrimonial and criminal matters. Jury trial experience.

Village attorney for Village of Brockport, New York. Counsels Village Board of Trustees Zoning Board of Appeals, Planning Board and ex officio member of Ethics Board.

Prosecutes Village Code violations from initial charge through appeal, advises Village officers and departments with regard to law enforcement and miscellaneous municipal law matters.

Counsel to Zoning Board of Appeals and Planning Board of Village of Webster, New York.

Advise both boards on interpretation of Village Code and State and Federal laws affecting applications before the boards; drafting amendments to Village Code, and prosecuting zoning violations.

Associate

HARRIS BEACH & WILCOX

1989 – 1991 (2 years) Rochester, New York Area

Represented local governments and private parties in connection with secured loans, business development, business organization, tax and general business matters.

Attorney

Winthrop Stimson

1988 – 1989 (1 year)

Represented lenders and corporations in New York City, New York State, regional, interstate and international transactions; coordinated with intra-firm practice area groups to form transaction teams for corporate stock-driven and asset-based transactions, workouts of non-performing loans, purchase, sale and leasing of real property.

Attorney

Levinson & Passe

1987 – 1988 (1 year)

Boutique Midtown Manhattan law firm specializing in commercial real property transactions. Worked closely with real property developers and investors, maintaining heavy client contact and daily interactions with mortgage lenders, property managers and business tenants in connection with a broad range of legal services affecting real property.

Endre Süli

(also, Endre Suli) is Professor of Numerical Analysis in the Mathematical Institute, University of Oxford, Fellow and Tutor in Mathematics at Worcester College, Oxford, and Supernumerary Fellow of Linacre College, Oxford. He was educated at the University of Belgrade and, as a British Council Visiting Student, at the University of Reading and St Catherine’s College, Oxford. His research is concerned with the mathematical analysis of numerical algorithms for nonlinear partial differential equations.

Süli is Foreign Member of the Serbian Academy of Sciences and Arts (2009) and Fellow of the European Academy of Sciences (2010). He was invited speaker at the International Congress of Mathematicians in Madrid in 2006[1] and was Chair of the Society for the Foundations of Computational Mathematics (2002–2005).[2] Since 2005 Süli has been co-Editor-in-Chief of the IMA Journal of Numerical Analysis.[3] He is a member of the Scientific Steering Committee of the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge and of the Scientific Advisory Board of the Archimedes Center for Modeling, Analysis and Computation at the University of Crete.

目测都是牛津大学的高人。

顶礼膜拜！

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