《数值分析导论(及答案)》(An Introduction to Numerical Analysis & Solutions)First published 2003[PDF]

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原名An Introduction to Numerical Analysis & Solutions
版本First published 2003

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Endre S¨uli and David F. Mayers
David F. Mayer's Overview

Adjunct Professor at Monroe Community College
Partner at Harris Chesworth O'Brien
Attorney at Winthrop Stimson
Attorney at Levinson & Passe
Syracuse University College of Law
University of Wisconsin-Superior
4 people have recommended David F.
227 connections
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

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;
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)

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.

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

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.

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.

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.
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.
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.
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.
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.



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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






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