concise numerical mathematics graduate studies in mathematics z

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Concise Numerical Mathematics

Author : Robert Plato
ISBN : 9780821829530
Genre : Mathematics
File Size : 81. 11 MB
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This textbook is a concise introduction to the fundamental concepts and methods of numerical mathematics. The author manages to cover the many important topics while avoiding redundancies and using well-chosen examples and exercises. The exposition is supplemented by numerous figures. Work estimates and pseudo codes are provided for many algorithms, which can be easily converted to computer programs. Topics covered include interpolation, the fast Fourier transform, iterative methods for solving systems of linear and nonlinear equations, numerical methods for solving ODEs, numerical methods for matrix eigenvalue problems, approximation theory, and computer arithmetic. The book is suitable as a text for a first course in numerical methods for mathematics students or students in neighboring fields, such as engineering, physics, and computer science. In general, the author assumes only a knowledge of calculus and linear algebra.

Collocation Methods For Volterra Integral And Related Functional Differential Equations

Author : Hermann Brunner
ISBN : 0521806151
Genre : Mathematics
File Size : 42. 67 MB
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Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present book introduces the reader to the general principles underlying these methods and then describes in detail their convergence properties when applied to ordinary differential equations, functional equations with (Volterra type) memory terms, delay equations, and differential-algebraic and integral-algebraic equations. Each chapter starts with a self-contained introduction to the relevant theory of the class of equations under consideration. Numerous exercises and examples are supplied, along with extensive historical and bibliographical notes utilising the vast annotated reference list of over 1300 items. In sum, Hermann Brunner has written a treatise that can serve as an introduction for students, a guide for users, and a comprehensive resource for experts.

Crc Concise Encyclopedia Of Mathematics Second Edition

Author : Eric W. Weisstein
ISBN : 9781420035223
Genre : Mathematics
File Size : 90. 33 MB
Format : PDF, ePub
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Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the dedication of author Eric Weisstein to collecting, cataloging, and referencing mathematical facts, formulas, and definitions. He has now updated most of the original entries and expanded the Encyclopedia to include 1000 additional pages of illustrated entries. The accessibility of the Encyclopedia along with its broad coverage and economical price make it attractive to the widest possible range of readers and certainly a must for libraries, from the secondary to the professional and research levels. For mathematical definitions, formulas, figures, tabulations, and references, this is simply the most impressive compendium available.

A Concise History Of Mathematics

Author : Dirk J. Struik
ISBN : 9780486138886
Genre : Science
File Size : 44. 79 MB
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Compact, well-written survey ranges from the ancient Near East to 20th-century computer theory, covering Archimedes, Pascal, Gauss, Hilbert, and many others. "A work which is unquestionably one of the best." — Nature.

Extenics And Innovation Methods

Author : Wen Cai
ISBN : 9780203797303
Genre : Technology & Engineering
File Size : 20. 48 MB
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Society forges ahead in the process of solving various contradictory problems and it is ceaselessly innovating. It is the desire of mankind to use computers and computing networks to help deal with contradictory problems and to conduct innovative activities. Using formal models to discuss object extension and the possibility of change, as well as the rules and methods for innovation, Extenics is applied to solving contradictory problems and has become the basic theory, method and instrument to achieve this goal. In the 30 years since the foundation of Extenics, researchers have built relatively complete theoretical systems —‘extension theory’, studied formal and modeling innovation methods —‘extension innovation methods’, and launched the applications in various fields such as information, design, automation and management etc. —‘extension engineering’. Extension theory, the extension innovation method and extension engineering jointly constitute the new discipline—Extenics. At the same time, the practical activities of engineering technology and management promote the integration of various innovation methods such as TRIZ and brainstorming etc. This book collects together, from scholars in various fields, the research achievements in Extenics and innovation methods, in order to facilitate and promote the development of Extenics and the various innovation theories and methods, as well as to improve its innovative capacity in academic and business circles.

An Introduction To Phase Integral Methods

Author : John Heading
ISBN : 9780486497426
Genre : Mathematics
File Size : 82. 83 MB
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The phase-integral method in mathematics, also known as the Wentzel-Kramers-Brillouin (WKB) method, is the focus of this introductory treatment. Author John Heading successfully steers a course between simplistic and rigorous approaches to provide a concise overview for advanced undergraduates and graduate students in mathematics and physics. Since the number of applications is vast, the text considers only a brief selection of topics and emphasizes the method itself rather than detailed applications. The process, once derived, is shown to be one of essential simplicity that involves merely the application of certain well-defined rules. Starting with a historical survey of the problem and its solutions, subjects include the Stokes phenomenon, one and two transition points, and applications to physical problems. An appendix and bibliography conclude the text.

Engineering Mathematics With Examples And Applications

Author : Xin-She Yang
ISBN : 9780128099025
Genre : Mathematics
File Size : 44. 52 MB
Format : PDF, Kindle
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Engineering Mathematics with Examples and Applications provides a compact and concise primer in the field, starting with the foundations, and then gradually developing to the advanced level of mathematics that is necessary for all engineering disciplines. Therefore, this book's aim is to help undergraduates rapidly develop the fundamental knowledge of engineering mathematics. The book can also be used by graduates to review and refresh their mathematical skills. Step-by-step worked examples will help the students gain more insights and build sufficient confidence in engineering mathematics and problem-solving. The main approach and style of this book is informal, theorem-free, and practical. By using an informal and theorem-free approach, all fundamental mathematics topics required for engineering are covered, and readers can gain such basic knowledge of all important topics without worrying about rigorous (often boring) proofs. Certain rigorous proof and derivatives are presented in an informal way by direct, straightforward mathematical operations and calculations, giving students the same level of fundamental knowledge without any tedious steps. In addition, this practical approach provides over 100 worked examples so that students can see how each step of mathematical problems can be derived without any gap or jump in steps. Thus, readers can build their understanding and mathematical confidence gradually and in a step-by-step manner. Covers fundamental engineering topics that are presented at the right level, without worry of rigorous proofs Includes step-by-step worked examples (of which 100+ feature in the work) Provides an emphasis on numerical methods, such as root-finding algorithms, numerical integration, and numerical methods of differential equations Balances theory and practice to aid in practical problem-solving in various contexts and applications

Numerical Mathematics

Author : Alfio Quarteroni
ISBN : 9783540498094
Genre : Mathematics
File Size : 48. 25 MB
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This book provides the mathematical foundations of numerical methods and demonstrates their performance on examples, exercises and real-life applications. This is done using the MATLAB software environment, which allows an easy implementation and testing of the algorithms for any specific class of problems. The book is addressed to students in Engineering, Mathematics, Physics and Computer Sciences. In the second edition of this extremely popular textbook on numerical analysis, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been

Numerical Solution Of Ordinary Differential Equations

Author : Kendall Atkinson
ISBN : 9781118164525
Genre : Mathematics
File Size : 58. 19 MB
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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.

An Introduction To Computational Engineering With Matlab

Author : Xin-She Yang
ISBN : 9781904602521
Genre : Computers
File Size : 73. 31 MB
Format : PDF
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This book strives to provide a concise introduction to computational engineering by introducing a wide range of numerical methods commonly used, such as finite difference methods, finite volume methods, finite element methods, and virtual bee algorithms. (Computer Books)

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