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2012年

作者： Cox David A.

Green's functions and boundary value problems / 3rd ed.

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2011年

作者： Stakgold Ivar.

Numerical Analysis of Partial Differential Equations 1

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丛书名： pure and applied mathematics : a wiley series of texts, monographs, and tracts

2011年

作者： S. H. Lui

ISBN: (数字)9781118111130

ISBN: (纸本)9780470647288

A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.

关键词： partial differential equations PDE PDEs how to solve partial differential equations how to solve PDEs discretization techniques finite difference finite elements spectral methods Poisson equation elliptic PDE elliptic PDEs elliptic partial differential equations numerical linear algebra nonlinear problems infinite domains

Numerical Solution of Ordinary Differential Equations 1

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丛书名： pure and applied mathematics: a wiley series of texts, monographs and tracts

2009年

作者： Atkinson, Kendall E./ Han, Weimin/ Stewart, David

ISBN: (数字)9781118164495

ISBN: (纸本)9780470042946

A concise introduction to numerical methodsand the mathematical framework neededto understand their performance Numerical Solution of Ordinary Differential Equations presents a complete and easy-to-follow introduction to classical topics in the numerical solution of ordinary differential equations. The book's approach not only explains the presented mathematics, but also helps readers understand how these numerical methods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringing together and categorizing different types of problems in order to help readers comprehend the applications of ordinary differential equations. In addition, the authors' collective academic experience ensures a coherent and accessible discussion of key topics, including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to test and build their knowledge of the presented methods, and a related Web site features MATLAB® programs that facilitate the exploration of numerical methods in greater depth. Detailed references outline additional literature on both analytical and numerical aspects of ordinary differential equations for further exploration of individual topics. Numerical Solution of Ordinary Differential Equations is an excellent textbook for courses on the numerical solution of differential equations at the upper-undergraduate and beginning graduate levels. It also serves as a valuable reference for researchers in the fields of mathematics and engineering.

关键词： Differential equations

An introduction to nonlinear partial differential equations / 2nd ed.

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2008年

作者： Logan J. David

Linear algebra and its applications / 2nd ed.

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2007年

作者： Lax Peter D.

The mathematics of infinity : a guide to great ideas /

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2006年

作者： Faticoni Theodore G.

Theorems, Corollaries, Lemmas, and Methods of Proof 1

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丛书名： pure and applied mathematics: a wiley series of texts, monographs and tracts

2006年

作者： Richard J. Rossi

ISBN: (数字)9781118031575

ISBN: (纸本)9780470042953

A hands-on introduction to the tools needed for rigorous and theoretical mathematical reasoning Successfully addressing the frustration many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, Theorems, Corollaries, Lemmas, and Methods of Proof equips students with the tools needed to succeed while providing a firm foundation in the axiomatic structure of modern mathematics. This essential book: * Clearly explains the relationship between definitions, conjectures, theorems, corollaries, lemmas, and proofs * Reinforces the foundations of calculus and algebra * Explores how to use both a direct and indirect proof to prove a theorem * Presents the basic properties of real numbers * Discusses how to use mathematical induction to prove a theorem * Identifies the different types of theorems * Explains how to write a clear and understandable proof * Covers the basic structure of modern mathematics and the key components of modern mathematics A complete chapter is dedicated to the different methods of proof such as forward direct proofs, proof by contrapositive, proof by contradiction, mathematical induction, and existence proofs. In addition, the author has supplied many clear and detailed algorithms that outline these proofs. Theorems, Corollaries, Lemmas, and Methods of Proof uniquely introduces scratch work as an indispensable part of the proof process, encouraging students to use scratch work and creative thinking as the first steps in their attempt to prove a theorem. Once their scratch work successfully demonstrates the truth of the theorem, the proof can be written in a clear and concise fashion. The basic structure of modern mathematics is discussed, and each of the key components of modern mathematics is defined. Numerous exercises are included in each chapter, covering a wide range of topics with varied levels of difficulty. Intended as a main text for mathematics courses such as Methods of

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Computational Methods of Linear Algebra, Second Edition 2nd ed.

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丛书名： pure and applied mathematics: A wiley-Interscience series of texts, monographs and tracts

2005年

作者： Granville Sewell

ISBN: (数字)9780471742142

ISBN: (纸本)9780471735793

Learn to write programs to solve linear algebraic problems The Second Edition of this popular textbook provides a highly accessible introduction to the numerical solution of linear algebraic problems. Readers gain a solid theoretical foundation for all the methods discussed in the text and learn to write FORTRAN90 and MATLAB(r) programs to solve problems. This new edition is enhanced with new material and pedagogical tools, reflecting the author's hands-on teaching experience, including: * A new chapter covering modern supercomputing and parallel programming * Fifty percent more examples and exercises that help clarify theory and demonstrate real-world applications * MATLAB(r) versions of all the FORTRAN90 programs * An appendix with answers to selected problems The book starts with basic definitions and results from linear algebra that are used as a foundation for later chapters. The following four chapters present and analyze direct and iterative methods for the solution of linear systems of equations, linear least-squares problems, linear eigenvalue problems, and linear programming problems. Next, a chapter is devoted to the fast Fourier transform, a topic not often covered by comparable texts. The final chapter features a practical introduction to writing computational linear algebra software to run on today's vector and parallel supercomputers. Highlighted are double-precision FORTRAN90 subroutines that solve the problems presented in the text. The subroutines are carefully documented and readable, allowing students to follow the program logic from start to finish. MATLAB(r) versions of the codes are listed in an appendix. Machine-readable copies of the FORTRAN90 and MATLAB(r) codes can be downloaded from the text's accompanying Web site. With its clear style and emphasis on problem solving, this is a superior textbook for upper-level undergraduates and graduate students.

关键词： Algebras Linear Textbooks.

The numerical solution of ordinary and partial differential equations / 2nd ed.

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2005年

作者： Sewell Granville.