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A Concise Introduction To Numerical Analysis

Author: A. C. Faul
Publisher: CRC Press
ISBN: 1498712215
Size: 29.89 MB
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This textbook provides an accessible and concise introduction to numerical analysis for upper undergraduate and beginning graduate students from various backgrounds. It was developed from the lecture notes of four successful courses on numerical analysis taught within the MPhil of Scientific Computing at the University of Cambridge. The book is easily accessible, even to those with limited knowledge of mathematics. Students will get a concise, but thorough introduction to numerical analysis. In addition the algorithmic principles are emphasized to encourage a deeper understanding of why an algorithm is suitable, and sometimes unsuitable, for a particular problem. A Concise Introduction to Numerical Analysis strikes a balance between being mathematically comprehensive, but not overwhelming with mathematical detail. In some places where further detail was felt to be out of scope of the book, the reader is referred to further reading. The book uses MATLAB® implementations to demonstrate the workings of the method and thus MATLAB's own implementations are avoided, unless they are used as building blocks of an algorithm. In some cases the listings are printed in the book, but all are available online on the book’s page at www.crcpress.com. Most implementations are in the form of functions returning the outcome of the algorithm. Also, examples for the use of the functions are given. Exercises are included in line with the text where appropriate, and each chapter ends with a selection of revision exercises. Solutions to odd-numbered exercises are also provided on the book’s page at www.crcpress.com. This textbook is also an ideal resource for graduate students coming from other subjects who will use numerical techniques extensively in their graduate studies.

Mathematical Analysis

Author: Bernd S. W. Schröder
Publisher: John Wiley & Sons
ISBN: 9780470226766
Size: 67.97 MB
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A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.

A Short Introduction To Numerical Analysis

Author: M. V. Wilkes
Publisher: CUP Archive
ISBN: 9780521094122
Size: 15.92 MB
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This short book sets out the principles of the methods commonly employed in obtaining numerical solutions to mathematical equations and shows how they are applied in solving particular types of equations. Now that computing facilities are available to most universities, scientific and engineering laboratories and design shops, an introduction to numerical method is an essential part of the training of scientists and engineers. A course on the lines of Professor Wilkes's book is given to graduate or undergraduate students of mathematics, the physical sciences and engineering at many universities and the number will increase. By concentrating on the essentials of his subject and giving it a modern slant, Professor Wilkes has written a book that is both concise and that covers the needs of a great many users of digital computers; it will serve also as a sound introduction for those who need to consult more detailed works.

Elementary Numerical Analysis

Author: Kendall E. Atkinson
Publisher: Wiley
ISBN:
Size: 66.52 MB
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A concise introduction to numerical analysis for students in the sciences, mathematics, and engineering. In addition to coverage of all standard topics, it explores approximation methods, construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic. Computer programming applications are given in Fortran 77. Features numerous problems and exercises at the end of each section.

A Concise Introduction To Geometric Numerical Integration

Author: Sergio Blanes
Publisher: CRC Press
ISBN: 1315354861
Size: 52.12 MB
Format: PDF, Docs
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Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.

A Friendly Introduction To Numerical Analysis

Author: Brian Bradie
Publisher: Prentice Hall
ISBN: 9780130130549
Size: 67.10 MB
Format: PDF, ePub
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This reader-friendly introduction to the fundamental concepts and techniques of numerical analysis/numerical methods develops concepts and techniques in a clear, concise, easy-to- read manner, followed by fully-worked examples. Application problems drawn from the literature of many different fields prepares readers to use the techniques covered to solve a wide variety of practical problems. Rootfinding. Systems of Equations. Eigenvalues and Eigenvectors. Interpolation and Curve Fitting. Numerical Differentiation and Integration. Numerical Methods for Initial Value Problems of Ordinary Differential Equations. Second-Order One-Dimensional Two-Point Boundary Value Problems. Finite Difference Method for Elliptic Partial Differential Equations. Finite Difference Method for Parabolic Partial Differential Equations. Finite Difference Method for Hyperbolic Partial Differential Equations and the Convection-Diffusion Equation. For anyone interested in numerical analysis/methods and their applications in many fields

Introduction To Numerical Analysis

Author: Alastair Wood
Publisher: Addison Wesley
ISBN:
Size: 41.11 MB
Format: PDF, Mobi
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Author Alastair Wood provides a clear and concise book for novice numerical analysts. Computer based experiments allow readers to learn by doing. Methods are developed with sufficient background, allowing readers to see why a method works and when a method does not work. Wood offers an introduction to the more basic theoretical elements, as well as generating practical skills. Computer skills and real applications are stressed as Wood explores such topics as the Taylor Series, Maclaurin Series, Jacobi Iteration and Gauss-Seidel iteration. For novice Numerical Analysts.

Introduction To Numerical Analysis

Author: J. Stoer
Publisher: Springer Science & Business Media
ISBN: 1475755929
Size: 69.19 MB
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This book is based on a one-year introductory course on numerical analysis given by the authors at several universities in Germany and the United States. The authors concentrate on methods which can be worked out on a digital computer. For important topics, algorithmic descriptions (given more or less formally in ALGOL 60), as well as thorough but concise treatments of their theoretical founda tions, are provided. Where several methods for solving a problem are presented, comparisons of their applicability and limitations are offered. Each comparison is based on operation counts, theoretical properties such as convergence rates, and, more importantly, the intrinsic numerical properties that account for the reliability or unreliability of an algorithm. Within this context, the introductory chapter on error analysis plays a special role because it precisely describes basic concepts, such as the numerical stability of algorithms, that are indispensable in the thorough treatment of numerical questions. The remaining seven chapters are devoted to describing numerical methods in various contexts. In addition to covering standard topics, these chapters encom pass some special subjects not usually found in introductions to numerical analysis. Chapter 2, which discusses interpolation, gives an account of modem fast Fourier transform methods. In Chapter 3, extrapolation techniques for spe~d ing up the convergence of discretization methods in connection with Romberg integration are explained at length.

Numerical Solution Of Ordinary Differential Equations

Author: Kendall Atkinson
Publisher: John Wiley & Sons
ISBN: 1118164520
Size: 22.12 MB
Format: PDF, Docs
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A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures 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 testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.

Mathematical Methods For Physicists

Author: Tai L. Chow
Publisher: Cambridge University Press
ISBN: 9781139427968
Size: 57.85 MB
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This text is designed for an intermediate-level, two-semester undergraduate course in mathematical physics. It provides an accessible account of most of the current, important mathematical tools required in physics these days. It is assumed that the reader has an adequate preparation in general physics and calculus. The book bridges the gap between an introductory physics course and more advanced courses in classical mechanics, electricity and magnetism, quantum mechanics, and thermal and statistical physics. The text contains a large number of worked examples to illustrate the mathematical techniques developed and to show their relevance to physics. The book is designed primarily for undergraduate physics majors, but could also be used by students in other subjects, such as engineering, astronomy and mathematics.