Download or read book Fourier Series and Orthogonal Polynomials written by Dunham Jackson and published by Courier Corporation. This book was released on 2012-04-27 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Includes Pearson frequency functions, Jacobi, Hermite, and Laguerre polynomials, more.1941 edition.
Download or read book Fourier Series and Orthogonal Polynomials by Dunham Jackson written by Dunham Jackson and published by . This book was released on 1957 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fourier Series and Orthogonal Polynomials written by Dunham Jackson and published by Courier Corporation. This book was released on 2004-01-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Begins with a definition and explanation of the elements of Fourier series, and examines Legendre polynomials and Bessel functions. Also includes Pearson frequency functions and chapters on orthogonal, Jacobi, Hermite, and Laguerre polynomials, more. 1941 edition.
Download or read book Fourier Series and Orthogonal Polynomials written by Dunham Jackson and published by . This book was released on 2013-09 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fourier Series and Orthogonal Polynomials written by and published by . This book was released on 1941 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fourier Series in Orthogonal Polynomials written by Boris Osilenker and published by World Scientific. This book was released on 1999 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic coarse on general orthogonal polynomials and Fourie series in orthogonal polynomials. It consists of six chapters. Chapter 1 deals in essence with standard results from the university course on the function theory of a real variable and on functional analysis. Chapter 2 contains the classical results about the orthogonal polynomials (some properties, classical Jacobi polynomials and the criteria of boundedness). The main subject of the book is Fourier series in general orthogonal polynomials. Chapters 3 and 4 are devoted to some results in this topic (classical results about convergence and summability of Fourier series in L(2)micro; summability almost everywhere by the Cesaro means and the Poisson-Abel method for Fourier polynomial series are the subject of Chapters 4 and 5). The last chapter contains some estimates regarding the generalized shift operator and the generalized product formula, associated with general orthogonal polynomials. The starting point of the technique in Chapters 4 and 5 is the representations of bilinear and trilinear forms obtained by the author. The results obtained in these two chapters are new ones. Chapters 2 and 3 (and part of Chapter 1) will be useful to postgraduate students, and one can choose them for treatment. This book is intended for researchers (mathematicians and physicists) whose work involves function theory, functional analysis, harmonic analysis and approximation theory.
Download or read book Fourier Series and Orthogonol Polynomials written by Dunham Jackson and published by . This book was released on 1957 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of Approximation written by Dunham Jackson and published by American Mathematical Soc.. This book was released on 1930-12-31 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Orthogonal Polynomials written by Theodore S Chihara and published by Courier Corporation. This book was released on 2014-07-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some specific systems of orthogonal polynomials. Numerous examples and exercises, an extensive bibliography, and a table of recurrence formulas supplement the text.
Download or read book Fourier Series and Orthogonal Functions written by Harry F. Davis and published by Courier Corporation. This book was released on 2012-09-05 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This incisive text deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. Directed to advanced undergraduate and graduate students in mathematics as well as in physics and engineering, the book requires no prior knowledge of partial differential equations or advanced vector analysis. Students familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations will find the text both accessible and challenging. The first three chapters of the book address linear spaces, orthogonal functions, and the Fourier series. Chapter 4 introduces Legendre polynomials and Bessel functions, and Chapter 5 takes up heat and temperature. The concluding Chapter 6 explores waves and vibrations and harmonic analysis. Several topics not usually found in undergraduate texts are included, among them summability theory, generalized functions, and spherical harmonics. Throughout the text are 570 exercises devised to encourage students to review what has been read and to apply the theory to specific problems. Those preparing for further study in functional analysis, abstract harmonic analysis, and quantum mechanics will find this book especially valuable for the rigorous preparation it provides. Professional engineers, physicists, and mathematicians seeking to extend their mathematical horizons will find it an invaluable reference as well.
Download or read book Handbook of Fourier Analysis Its Applications written by Robert J. Marks and published by Oxford University Press. This book was released on 2009-01-08 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal processing and related multidimensional transform theory, and quantum physics to elementary deterministic finance and even the foundations of western music theory.
Download or read book The Collected Scientific Papers of Paul A Samuelson written by Paul Anthony Samuelson and published by MIT Press. This book was released on 1966 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: "It is a measure of Professor Samuelson's preeminence that the sheer scale of his work should be so much taken for granted," observes a reviewer in the Economist who goes on to note that "a cynic might add that it would have been better for Professor Samuelson to write less merely to give others a chance to write at all." These volumes contain virtually all of Professor Paul A. Samuelson's contributions to economic theory through mid-1964 - a total of 129 papers. Included are his classic articles on such topics as revealed preference, factor-price equalization, and public goods; as well as some articles which until now have only been privately circulated or "buried" in Festschriften, such as "Market Mechanisms and Maximization" and "The Structure of a Minimum Equilibrium System." The articles have been grouped together into five books, compiled in two volumes. The books, in turn have been divided into sections, each of which contains articles on the same or closely related topics. Within the sections the articles are arranged chronologically. The graduate student and professional economist will welcome The Collected Scientific Papers of Paul A. Samuelson as a valuable addition to their libraries.
Download or read book Irrational Numbers written by Ivan Niven and published by American Mathematical Soc.. This book was released on 1985-12-31 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, Ivan Niven provides a masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments. The approximation of irrational numbers by rationals, up to such results as the best possible approximation of Hurwitz, is also given with elementary techniques. The last third of the monograph treats normal and transcendental numbers, including the transcendence of p and its generalization in the Lindermann theorem, and the Gelfond-Schneider theorem. Most of the material in the first two thirds of the book presupposes only calculus and beginning number theory. The book is almost wholly self-contained. The results needed from analysis and algebra are central and well-known theorems, and complete references to standard works are given to help the beginner. The chapters are, for the most part, independent. There is a set of notes at the end of each chapter citing the main sources used by the author and suggesting further reading.
Download or read book Invitation to Classical Analysis written by Peter L. Duren and published by American Mathematical Soc.. This book was released on 2012 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a rigorous treatment of selected topics in classical analysis, with many applications and examples. The exposition is at the undergraduate level, building on basic principles of advanced calculus without appeal to more sophisticated techniques of complex analysis and Lebesgue integration. Among the topics covered are Fourier series and integrals, approximation theory, Stirling's formula, the gamma function, Bernoulli numbers and polynomials, the Riemann zeta function, Tauberian theorems, elliptic integrals, ramifications of the Cantor set, and a theoretical discussion of differential equations including power series solutions at regular singular points, Bessel functions, hypergeometric functions, and Sturm comparison theory. Preliminary chapters offer rapid reviews of basic principles and further background material such as infinite products and commonly applied inequalities. This book is designed for individual study but can also serve as a text for second-semester courses in advanced calculus. Each chapter concludes with an abundance of exercises. Historical notes discuss the evolution of mathematical ideas and their relevance to physical applications. Special features are capsule scientific biographies of the major players and a gallery of portraits. Although this book is designed for undergraduate students, others may find it an accessible source of information on classical topics that underlie modern developments in pure and applied mathematics.
Download or read book Vectors and Matrices written by Cyrus Colton MacDuffee and published by American Mathematical Soc.. This book was released on 1943-12-31 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1943, a course in linear algebra did not yet exist as a standard part of the undergraduate curriculum. It would be another twenty years before that would become common. It is, however, easy to identify the defining features of that course in this volume. Start with the idea of solving linear systems; change the point of view to that of transformations on vector spaces; recognize similarity as an essential classifying principle; and catalogue the canonical forms (Jordan normal form) of the transformations. All of this is here but with a decided, old-fashioned, algebraic accent—there is only one figure in the entire text.
Download or read book From Error Correcting Codes Through Sphere Packings to Simple Groups written by Thomas M. Thompson and published by American Mathematical Soc.. This book was released on 1983-12-31 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book traces a remarkable path of mathematical connections through seemingly disparate topics. Frustrations with a 1940's electro-mechanical computer at a premier research laboratory begin this story. Subsequent mathematical methods of encoding messages to ensure correctness when transmitted over noisy channels lead to discoveries of extremely efficient lattice packings of equal-radius balls, especially in 24-dimensional space. In turn, this highly symmetric lattice, with each point neighboring exactly 196,560 other points, suggested the possible presence of new simple groups as groups of symmetries. Indeed, new groups were found and are now part of the "Enormous Theorem"—the classification of all simple groups whose entire proof runs some 10,000+ pages—and these connections, along with the fascinating history and the proof of the simplicity of one of those "sporatic" simple groups, are presented at an undergraduate mathematical level.
Download or read book The Schwarz Function and Its Applications written by Philip J. Davis and published by American Mathematical Soc.. This book was released on 1974-12-31 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: H. A. Schwarz showed us how to extend the notion of reflection in straight lines and circles to reflection in an arbitrary analytic arc. Notable applications were made to the symmetry principle and to problems of analytic continuation. Reflection, in the hands of Schwarz, is an antianalytic mapping. By taking its complex conjugate, we arrive at an analytic function that we have called here the Schwarz Function of the analytic arc. This function is worthy of study in its own right and this essay presents such a study. In dealing with certain familiar topics, the use of the Schwarz Function lends a point of view, a clarity and elegance, and a degree of generality which might otherwise be missing. It opens up a line of inquiry which has yielded numerous interesting things in complex variables; it illuminates some functional equations and a variety of iterations which interest the numerical analyst. The perceptive reader will certainly find here some old wine in relabelled bottles. But one of the principles of mathematical growth is that the relabelling process often suggests a new generation of problems. Means become ends; the medium rapidly becomes the message. This book is not wholly self-contained. Readers will find that they should be familiar with the elementary portions of linear algebra and of the theory of functions of a complex variable.
