A Concise Introduction To Numerical Analysis

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A Concise Introduction to Numerical Analysis

A. C. Faul
A Concise Introduction to Numerical Analysis Book PDF

Author : A. C. Faul
Publisher : CRC Press
Page : 161 pages
File Size : 42,5 Mb
Release : 2018-10-24
Category : Mathematics
ISBN : 9781498712217

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A Concise Introduction to Numerical Analysis by A. C. Faul Pdf

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.

A Concise Introduction to Numerical Analysis

A. C. Faul
A Concise Introduction to Numerical Analysis Book PDF

Author : A. C. Faul
Publisher : CRC Press
Page : 292 pages
File Size : 41,9 Mb
Release : 2018-10-24
Category : Mathematics
ISBN : 9781315362328

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A Concise Introduction to Numerical Analysis by A. C. Faul Pdf

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

Bernd S. W. Schröder
Mathematical Analysis Book PDF

Author : Bernd S. W. Schröder
Publisher : John Wiley & Sons
Page : 584 pages
File Size : 48,8 Mb
Release : 2008-01-28
Category : Mathematics
ISBN : 0470226765

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Mathematical Analysis by Bernd S. W. Schröder Pdf

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.

Introduction to Numerical Analysis

Josef Stoer,R. Bulirsch
Introduction to Numerical Analysis Book PDF

Author : Josef Stoer,R. Bulirsch
Publisher : Springer Science & Business Media
Page : 766 pages
File Size : 45,8 Mb
Release : 2002-08-21
Category : Mathematics
ISBN : 9780387954523

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Introduction to Numerical Analysis by Josef Stoer,R. Bulirsch Pdf

New edition of a well-known classic in the field; Previous edition sold over 6000 copies worldwide; Fully-worked examples; Many carefully selected problems

A Concise Introduction to Geometric Numerical Integration

Sergio Blanes,Fernando Casas
A Concise Introduction to Geometric Numerical Integration Book PDF

Author : Sergio Blanes,Fernando Casas
Publisher : CRC Press
Page : 218 pages
File Size : 42,8 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781315354866

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A Concise Introduction to Geometric Numerical Integration by Sergio Blanes,Fernando Casas Pdf

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.

An Introduction to Numerical Methods and Analysis

James F. Epperson
An Introduction to Numerical Methods and Analysis Book PDF

Author : James F. Epperson
Publisher : John Wiley & Sons
Page : 614 pages
File Size : 45,6 Mb
Release : 2013-10-07
Category : Mathematics
ISBN : 9781118367599

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An Introduction to Numerical Methods and Analysis by James F. Epperson Pdf

Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises."—Zentralblatt MATH ". . . carefully structured with many detailed worked examples."—The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and the Second Edition also features: Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises Widespread exposure and utilization of MATLAB An appendix that contains proofs of various theorems and other material The book is an ideal textbook for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.

A Concise Introduction to Geometric Numerical Integration

Sergio Blanes,Fernando Casas
A Concise Introduction to Geometric Numerical Integration Book PDF

Author : Sergio Blanes,Fernando Casas
Publisher : CRC Press
Page : 218 pages
File Size : 54,9 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781482263442

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A Concise Introduction to Geometric Numerical Integration by Sergio Blanes,Fernando Casas Pdf

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.

Numerical Linear Algebra

Folkmar Bornemann
Numerical Linear Algebra Book PDF

Author : Folkmar Bornemann
Publisher : Springer
Page : 153 pages
File Size : 40,7 Mb
Release : 2018-01-29
Category : Mathematics
ISBN : 9783319742229

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Numerical Linear Algebra by Folkmar Bornemann Pdf

This book offers an introduction to the algorithmic-numerical thinking using basic problems of linear algebra. By focusing on linear algebra, it ensures a stronger thematic coherence than is otherwise found in introductory lectures on numerics. The book highlights the usefulness of matrix partitioning compared to a component view, leading not only to a clearer notation and shorter algorithms, but also to significant runtime gains in modern computer architectures. The algorithms and accompanying numerical examples are given in the programming environment MATLAB, and additionally – in an appendix – in the future-oriented, freely accessible programming language Julia. This book is suitable for a two-hour lecture on numerical linear algebra from the second semester of a bachelor's degree in mathematics.

Mathematical Analysis: A Concise Introduction

Jiongmin Yong
Mathematical Analysis A Concise Introduction Book PDF

Author : Jiongmin Yong
Publisher : World Scientific
Page : 274 pages
File Size : 53,6 Mb
Release : 2020-12-29
Category : Mathematics
ISBN : 9789811221651

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Mathematical Analysis: A Concise Introduction by Jiongmin Yong Pdf

Mathematical analysis serves as a common foundation for many research areas of pure and applied mathematics. It is also an important and powerful tool used in many other fields of science, including physics, chemistry, biology, engineering, finance, and economics. In this book, some basic theories of analysis are presented, including metric spaces and their properties, limit of sequences, continuous function, differentiation, Riemann integral, uniform convergence, and series.After going through a sequence of courses on basic calculus and linear algebra, it is desirable for one to spend a reasonable length of time (ideally, say, one semester) to build an advanced base of analysis sufficient for getting into various research fields other than analysis itself, and/or stepping into more advanced levels of analysis courses (such as real analysis, complex analysis, differential equations, functional analysis, stochastic analysis, amongst others). This book is written to meet such a demand. Readers will find the treatment of the material is as concise as possible, but still maintaining all the necessary details.

An Introduction to Numerical Analysis

Endre Süli,David F. Mayers
An Introduction to Numerical Analysis Book PDF

Author : Endre Süli,David F. Mayers
Publisher : Cambridge University Press
Page : 440 pages
File Size : 41,9 Mb
Release : 2003-08-28
Category : Mathematics
ISBN : 0521007941

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An Introduction to Numerical Analysis by Endre Süli,David F. Mayers Pdf

An introduction to numerical analysis combining rigour with practical applications, and providing numerous exercises plus solutions.

Introduction to Numerical Analysis

Francis Begnaud Hildebrand
Introduction to Numerical Analysis Book PDF

Author : Francis Begnaud Hildebrand
Publisher : Courier Corporation
Page : 704 pages
File Size : 42,9 Mb
Release : 1987-01-01
Category : Mathematics
ISBN : 0486653633

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Introduction to Numerical Analysis by Francis Begnaud Hildebrand Pdf

The ultimate aim of the field of numerical analysis is to provide convenient methods for obtaining useful solutions to mathematical problems and for extracting useful information from available solutions which are not expressed in tractable forms. This well-known, highly respected volume provides an introduction to the fundamental processes of numerical analysis, including substantial grounding in the basic operations of computation, approximation, interpolation, numerical differentiation and integration, and the numerical solution of equations, as well as in applications to such processes as the smoothing of data, the numerical summation of series, and the numerical solution of ordinary differential equations. Chapter headings include: l. Introduction 2. Interpolation with Divided Differences 3. Lagrangian Methods 4. Finite-Difference Interpolation 5. Operations with Finite Differences 6. Numerical Solution of Differential Equations 7. Least-Squares Polynomial Approximation In this revised and updated second edition, Professor Hildebrand (Emeritus, Mathematics, MIT) made a special effort to include more recent significant developments in the field, increasing the focus on concepts and procedures associated with computers. This new material includes discussions of machine errors and recursive calculation, increased emphasis on the midpoint rule and the consideration of Romberg integration and the classical Filon integration; a modified treatment of prediction-correction methods and the addition of Hamming's method, and numerous other important topics. In addition, reference lists have been expanded and updated, and more than 150 new problems have been added. Widely considered the classic book in the field, Hildebrand's Introduction to Numerical Analysis is aimed at advanced undergraduate and graduate students, or the general reader in search of a strong, clear introduction to the theory and analysis of numbers.

Introduction to Numerical Analysis

Alastair Wood
Introduction to Numerical Analysis Book PDF

Author : Alastair Wood
Publisher : Addison Wesley Longman
Page : 372 pages
File Size : 40,9 Mb
Release : 1999
Category : Numerical analysis
ISBN : PSU:000046232267

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Introduction to Numerical Analysis by Alastair Wood Pdf

P. 311.

Numerical Analysis

Rainer Kress
Numerical Analysis Book PDF

Author : Rainer Kress
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461205999

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Numerical Analysis by Rainer Kress Pdf

An introduction into numerical analysis for students in mathematics, physics, and engineering. Instead of attempting to exhaustively cover everything, the goal is to guide readers towards the basic ideas and general principles by way of the main and important numerical methods. The book includes the necessary basic functional analytic tools for the solid mathematical foundation of numerical analysis -- indispensable for any deeper study and understanding of numerical methods, in particular, for differential equations and integral equations. The text is presented in a concise and easily understandable fashion so as to be successfully mastered in a one-year course.

Numerical Methods

Anne Greenbaum,Tim P. Chartier
Numerical Methods Book PDF

Author : Anne Greenbaum,Tim P. Chartier
Publisher : Princeton University Press
Page : 471 pages
File Size : 51,8 Mb
Release : 2012-04-01
Category : Mathematics
ISBN : 9781400842674

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Numerical Methods by Anne Greenbaum,Tim P. Chartier Pdf

A rigorous and comprehensive introduction to numerical analysis Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects—design, analysis, or computer implementation—of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online. Clear and concise exposition of standard numerical analysis topics Explores nontraditional topics, such as mathematical modeling and Monte Carlo methods Covers modern applications, including information retrieval and animation, and classical applications from physics and engineering Promotes understanding of computational results through MATLAB exercises Provides flexibility so instructors can emphasize mathematical or applied/computational aspects of numerical methods or a combination Includes recent results on polynomial interpolation at Chebyshev points and use of the MATLAB package Chebfun Short discussions of the history of numerical methods interspersed throughout Supplementary materials available online

Introduction to Numerical Analysis

J. Stoer,R. Bulirsch
Introduction to Numerical Analysis Book PDF

Author : J. Stoer,R. Bulirsch
Publisher : Springer Science & Business Media
Page : 674 pages
File Size : 42,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475722727

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Introduction to Numerical Analysis by J. Stoer,R. Bulirsch Pdf

On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations.