An Atlas of Functions

This book comprehensively covers several hundred functions or function families.

Author: Keith B. Oldham

Publisher: Springer Science & Business Media

ISBN: 9780387488073

Category: Mathematics

Page: 748

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This book comprehensively covers several hundred functions or function families. In chapters that progress by degree of complexity, it starts with simple, integer-valued functions then moves on to polynomials, Bessel, hypergeometric and hundreds more.

Equator

The Windows-based Equator software is available as an integral part of the book An Atlas of Functions, Second Edition, although its utility is not limited to users of this book.

Author: Keith B. Oldham

Publisher: Springer

ISBN: 0387097732

Category: Mathematics

Page: 265

View: 953

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Equator is software designed to generate numerical values of over 200 mathematical functions in common use by engineers, scientists and others. Among the functions made available are simple ones such as cosines and binomial coefficients, as well as more complex examples such as Bessel functions and elliptic integrals. The Windows-based Equator software is available as an integral part of the book An Atlas of Functions, Second Edition, although its utility is not limited to users of this book. The Atlas is available in both print and electronic formats; full details can be found at www.springer.com. Equator is sold as a stand-alone unit, in part to benefit those who may access the electronic version of the Atlas through their library.

Zeta and Q Zeta Functions and Associated Series and Integrals

M. A. Nyblom, On the evaluation of a definite integral involving nested square root functions, Rocky Mountain J. Math. ... With Equator, the Atlas Function Calculator, Second edition [with 1 CD-ROM (Windows)], Springer, New York, 2009.

Author: H. M. Srivastava

Publisher: Elsevier

ISBN: 9780123852182

Category: Mathematics

Page: 657

View: 544

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Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions

Visual Complex Functions

K. B. Oldham, J. Myland, and J. Spanier, An Atlas of Functions: with Equator, the Atlas Function Calculator. (2nd ed.) Springer New York 2008. F.W.J. Olver, D.W. Lozier, R.F. Boisvert, Ch.W. Clark (executive editors), Digital Library of ...

Author: Elias Wegert

Publisher: Springer Science & Business Media

ISBN: 9783034801805

Category: Mathematics

Page: 360

View: 404

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This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations – so-called phase portraits – which visualize functions as images on their domains. Reading Visual Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course on complex analysis. With separate chapters on various construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes. In a second storyline, running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endow individual faces to analytic functions. Phase portraits enhance the intuitive understanding of concepts in complex analysis and are expected to be useful tools for anybody working with special functions – even experienced researchers may be inspired by the pictures to new and challenging questions. Visual Complex Functions may also serve as a companion to other texts or as a reference work for advanced readers who wish to know more about phase portraits.

Basic Complex Analysis A Comprehensive Course in Analysis Part 2A

... and J. Spanier, An Atlas of Functions. With Equator, the Atlas Function Calculator, 2nd edition, Springer, New York, 2009. (Cited on 214.) C. D. Olds, Continued Fractions, Random House, New York, 1963. (Cited on 304.) ...

Author: Barry Simon

Publisher: American Mathematical Soc.

ISBN: 9781470411008

Category: Mathematical analysis

Page: 641

View: 715

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A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.

Numerical methods for scientists and engineers

Oldham, K. B., Myland, J. C. and Spanier, J. (2009): An Atlas of Functions: with Equator, the Atlas Function Calculator, (2nd ed.) Springer, Berlin. Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P. (2007): Numerical ...

Author: H. M. Antia

Publisher: Springer

ISBN: 9789386279521

Category: Science

Page: 888

View: 508

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This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems. The main addition in the third edition is a new Chapter on Statistical Inferences. There is also some addition and editing in the next chapter on Approximations. With this addition 12 new programs have also been added.

Software Reliability Modeling

Mathematical systemability function approximations. ... Generalized markovian software reliability modeling and its alternative calculation. ... An atlas of functions, with equator, the atlas function calculator (2nd ed.).

Author: Shigeru Yamada

Publisher: Springer Science & Business Media

ISBN: 9784431545651

Category: Mathematics

Page: 90

View: 423

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Software reliability is one of the most important characteristics of software product quality. Its measurement and management technologies during the software product life cycle are essential to produce and maintain quality/reliable software systems. Part 1 of this book introduces several aspects of software reliability modeling and its applications. Hazard rate and nonhomogeneous Poisson process (NHPP) models are investigated particularly for quantitative software reliability assessment. Further, imperfect debugging and software availability models are discussed with reference to incorporating practical factors of dynamic software behavior. Three software management problems are presented as application technologies of software reliability models: the optimal software release problem, the statistical testing-progress control, and the optimal testing-effort allocation problem. Part 2 of the book describes several recent developments in software reliability modeling and their applications as quantitative techniques for software quality/reliability measurement and assessment. The discussion includes a quality engineering analysis of human factors affecting software reliability during the design review phase, which is the upper stream of software development, as well as software reliability growth models based on stochastic differential equations and discrete calculus during the testing phase, which is the lower stream. The final part of the book provides an illustration of quality-oriented software management analysis by applying the multivariate analysis method and the existing software reliability growth models to actual process monitoring data.

Experimental and Computational Mathematics

“Analytical models of optical refraction in the troposphere.” JOSA, 20 867–875. [46] K. Oldham, J. Myland, and J. Spanier (2009). An Atlas of Functions: With Equator, The Atlas Function Calculator, Springer-Verlag.

Author: Jonathan M. Borwein

Publisher: PSIpress

ISBN: 9781935638056

Category: Experimental mathematics

Page: 297

View: 722

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A quiet revolution in mathematical computing and scientific visualization took place in the latter half of the 20th century. These developments have dramatically enhanced modes of mathematical insight and opportunities for "exploratory" computational experimentation. This volume collects the experimental and computational contributions of Jonathan and Peter Borwein over the past quarter century.

Software Engineering Business Continuity and Education

I.: An Atlas of Functions: with Equator, the Atlas Function Calculator, 2nd edn. Springer, New York (2008) Goel, A.L., Okumoto, K.: Time-Dependent Error-Detection Rate Model for Software Reliability and Other Performance Measures.

Author: Tai-hoon Kim

Publisher: Springer Science & Business Media

ISBN: 9783642272066

Category: Computers

Page: 716

View: 750

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This book comprises selected papers of the International Conferences, ASEA, DRBC and EL 2011, held as Part of the Future Generation Information Technology Conference, FGIT 2011, in Conjunction with GDC 2011, Jeju Island, Korea, in December 2011. The papers presented were carefully reviewed and selected from numerous submissions and focuse on the various aspects of advances in software engineering and its Application, disaster recovery and business continuity, education and learning.