Download or read book Ten Place Tables of the Jacobian Elliptic Functions written by Henry E. Fettis and published by . This book was released on 1965 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Selected Topics in Mathematical Physics written by William A. Schwalm and published by Morgan & Claypool Publishers. This book was released on 2015-12-31 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first and second year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.
Download or read book Handbook of Tables for Elliptic Function Filters written by K.L. Su and published by Springer Science & Business Media. This book was released on 1990-06-30 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is inspired by occasional questions from my stu dents and coworkers as to how they can obtain easily the best network functions from which they can complete their filter design projects to satisfy certain criteria. They don't need any help to design the filter. They need only the network function. It appears that this crucial step can be a bottleneck to designers. This handbook is meant to supply the information for those who need a quick answer to a simple question of this kind. There are three most useful basic standard low-pass magnitude characteristics used in filter design. These are the Butterworth, the Chebyshev, and the elliptic characteristics. The Butterworth charac teristic is maximally flat at the origin. The Chebyshev characteristic gives equal-ripple variation in the pass band. The elliptic character istic gives equal-ripple variation in both the pass band and the stop band. The Butterworth and the Chebyshev characteristics are fairly easy to use, and formulas for their parameters are widely available and fairly easy to apply. The theory and derivation of formulas for the elliptic characteristic, however, are much more difficult to handle and understand. This is chiefly because their original development made use of the Jacobian elliptic functions, which are not familiar to most electrical engineers. Although there are several other methods of developing this characteristic, such as the potential analogy, the Chebyshev rational functions, and numerical techniques, most filter designers are as unfamiliar with these methods as they are with the elliptic functions.
Download or read book Tables of Jacobian Elliptic Functions Whose Arguments are Rational Fractions of the Quarter Period written by Alan Robert Curtis and published by . This book was released on 1964 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Elliptic Integrals for Engineers and Physicists written by Paul F. Byrd and published by Springer. This book was released on 2013-11-21 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineers and physicists are more and more encountering integrations involving nonelementary integrals and higher transeendental functions. Such integrations frequently involve (not always in immediately re cognizable form) elliptic functions and elliptic integrals. The numerous books written on elliptic integrals, while of great value to the student or mathematician, are not especially suitable for the scientist whose primary objective is the ready evaluation of the integrals that occur in his practical problems. As a result, he may entirely avoid problems which lead to elliptic integrals, or is likely to resort to graphical methods or other means of approximation in dealing with all but the siruplest of these integrals. It became apparent in the course of my work in theoretical aero dynamics that there was a need for a handbook embodying in convenient form a comprehensive table of elliptic integrals together with auxiliary formulas and numerical tables of values. Feeling that such a book would save the engineer and physicist much valuable time, I prepared the present volume.
Download or read book A 20 D Table of Jacobi s Nome and Its Inverse written by Henry E. Fettis and published by . This book was released on 1969 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jacobi's Nome q is given to twenty decimals as a function of the modulus-squared, k squared, the modular angle arc sin k, and the complementary modulus k' for k squared : 0(.001) 999; arc sin k : 0(.10) 89 degrees (.01) 89.99 degrees (.0002) 90 degrees; k' : 0001(.0001).02. The latter table also gives values of an approximation valid in this range to the order of (k') squared, as well as the ratio of the true and approximate values and second central differences of the latter ratio. The fourth table gives k and k' as functions of q for q = 0(.001).5. (Author).
Download or read book Elliptic Functions written by J. V. Armitage and published by Cambridge University Press. This book was released on 2006-09-28 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: In its first six chapters, this text presents the basic ideas and properties of the Jacobi elliptic functions as a historical essay. Accordingly, it is based on the idea of inverting integrals which arise in the theory of differential equations and, in particular, the differential equation that describes the motion of a simple pendulum. The later chapters present a more conventional approach to the Weierstrass functions and to elliptic integrals, and the reader is introduced to the richly varied applications of the elliptic and related functions.
Download or read book Handbook of Mathematical Functions with Formulas Graphs and Mathematical Tables written by Milton Abramowitz and published by . This book was released on 1964 with total page 1072 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elliptic Functions and Applications written by Derek F. Lawden and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject matter of this book formed the substance of a mathematical se am which was worked by many of the great mathematicians of the last century. The mining metaphor is here very appropriate, for the analytical tools perfected by Cauchy permitted the mathematical argument to penetra te to unprecedented depths over a restricted region of its domain and enabled mathematicians like Abel, Jacobi, and Weierstrass to uncover a treasurehouse of results whose variety, aesthetic appeal, and capacity for arousing our astonishment have not since been equaled by research in any other area. But the circumstance that this theory can be applied to solve problems arising in many departments of science and engineering graces the topic with an additional aura and provides a powerful argument for including it in university courses for students who are expected to use mathematics as a tool for technological investigations in later life. Unfortunately, since the status of university staff is almost wholly determined by their effectiveness as research workers rather than as teachers, the content of undergraduate courses tends to reflect those academic research topics which are currently popular and bears little relationship to the future needs of students who are themselves not destined to become university teachers. Thus, having been comprehensively explored in the last century and being undoubtedly difficult .
Download or read book Handbook of Mathematical Functions written by Milton Abramowitz and published by Courier Corporation. This book was released on 1965-01-01 with total page 1068 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive summary of mathematical functions that occur in physical and engineering problems
Download or read book Elliptic Functions According to Eisenstein and Kronecker written by Andre Weil and published by Springer Science & Business Media. This book was released on 1999 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawn from the Foreword: (...) On the other hand, since much of the material in this volume seems suitable for inclusion in elementary courses, it may not be superfluous to point out that it is almost entirely self-contained. Even the basic facts about trigonometric functions are treated ab initio in Ch. II, according to Eisenstein's method. It would have been both logical and convenient to treat the gamma -function similarly in Ch. VII; for the sake of brevity, this has not been done, and a knowledge of some elementary properties of T(s) has been assumed. One further prerequisite in Part II is Dirichlet's theorem on Fourier series, together with the method of Poisson summation which is only a special case of that theorem; in the case under consideration (essentially no more than the transformation formula for the theta-function) this presupposes the calculation of some classical integrals. (...) As to the final chapter, it concerns applications to number theory (...).
Download or read book Table of Integrals Series and Products written by I. S. Gradshteyn and published by Academic Press. This book was released on 2014-05-10 with total page 1207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.
Download or read book F nfstellige Tabellen zu den Elliptischen Funktionen Five Place Tables of Elliptical Functions written by Max Schuler and published by Springer. This book was released on 2013-12-11 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Applications of Elliptic Functions written by Sir George Greenhill and published by . This book was released on 1892 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Jacobian Elliptic Function Tables written by Louis Melville Milne-Thomson and published by . This book was released on 1950 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Five Place Tables of Elliptical Functions written by Max Schuler and published by . This book was released on 1955 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Projects and Publications written by United States. National Bureau of Standards. National Applied Mathematics Laboratories and published by . This book was released on 1949 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt:
