Download or read book Differential Operations Of Infinite Order With Real Arguments And Their Applications written by Dinh Nho Hao and published by World Scientific. This book was released on 1994-04-29 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the theory of infinite-order linear and nonlinear differential operators with several real arguments and their applications to problems of partial differential equations and numerical analysis.Part I develops the theory of pseudodifferential operators with real analytic symbols, the local representatives of which are linear differential operators of infinite order acting in the spaces of basic and generalized functions based on the duality of the spaces of real analytic functions and functionals. Applications to a variety of problems of PDEs and numerical analysis are given. Part II is devoted to the theory of Sobolev-Orlicz spaces of infinite order and the solvability of nonlinear partial differential equations with arbitrary nonlinearities.
Download or read book Advanced Calculus Revised Edition written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Download or read book Infinite Series and Products written by Demetrios P. Kanoussis and published by . This book was released on 2018-10-15 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a complete and self contained presentation on the fundamentals of Infinite Series and Products and has been designed to be an excellent supplementary textbook for University and College students in all areas of Math, Physics and Engineering.Infinite Series and Products is a branch of Applied Mathematics with an enormous range of applications in various areas of Applied Sciences and Engineering.The Theory of Infinite Series and Products relies heavily on the Theory of Infinite Sequences and therefore the reader of this text is urged to refresh his/her background on Sequences and related topics.In our e-book "Sequences of Real and Complex Numbers" the reader will find an excellent introduction to the subject that will help him/her to follow readily the matter developed in the current text.The content of this book is divided into 11 chapters.In Chapter 1 we introduce the Σ and the Π notation which is widely used to denote infinite series and infinite products, respectively. In Chapter 2 we present some basic, fundamental concepts and definitions pertaining to infinite series, such as convergent series, divergent series, the infinite geometric series, etc.In Chapter 3 we introduce the extremely important concept of Telescoping Series and show how this concept is used in order to find the sum of an infinite series in closed form (when possible). In this chapter we also present a list of Telescoping Trigonometric Series, which arise often on various applications.In Chapter 4 we develop some general Theorems on Infinite Series, for example deleting or inserting or grouping terms in a series, the Cauchy's necessary and sufficient condition for convergence, the widely used necessary test for convergence, the Harmonic Series, etc.In Chapter 5 we study the Convergence Test for Series with Positive Terms, i.e. the Comparison Test, the Limit Comparison Test, the D' Alembert's Test, the Cauchy's n-th Root Test, the Raabe's Test, the extremely important Cauchy's Integral Test, the Cauchy's Condensation Test etc.In Chapter 6 we study the Alternating Series and the investigation of such series with the aid of the Leibnitz's Theorem.In Chapter 7 we introduce and investigate the Absolutely Convergent Series and the Conditionally Convergent Series, state some Theorems on Absolute and Conditional Convergence and define the Cauchy Product of two absolutely convergent series.In Chapter 8 we give a brief review of Complex Numbers and Hyperbolic Functions, needed for the development of series from real to complex numbers. We define the Complex Numbers and their Algebraic Operations and give the three representations i.e. the Cartesian, the Polar and the Exponential representation of the Complex Numbers. The famous Euler's Formulas and the important De Moivre's Theorem are presented and various interesting applications are given. In this chapter we also define the so called Hyperbolic Functions of real and complex arguments.In Chapter 9 we introduce the theory of Series with Complex Terms, define the convergence in the complex plane and present a few important Theorems which are particularly useful for the investigation of series with complex terms.In Chapter 10 we define the Multiple Series and show how to treat simple cases of such series.In Chapter 11 we present the fundamentals of the Infinite Products, give the necessary and sufficient condition for the convergence of Infinite Products and define the Absolute and Conditional Convergence of Products. In particular in this chapter we present the Euler's product formula for the sine function and show how Euler used this product to solve the famous Basel problem.The 63 illustrative examples and the 176 characteristic problems are designed to help students sharpen their analytical skills on the subject.
Download or read book Sobolev Spaces of Infinite Order and Differential Equations written by Julii A. Dubinskii and published by Springer Science & Business Media. This book was released on 1986-12-31 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book KWIC Index for Numerical Algebra written by Alston Scott Householder and published by . This book was released on 1972 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Global Analysis written by Shiing-Shen Chern and published by American Mathematical Soc.. This book was released on 1970-12 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Fourier Series written by Rupert Lasser and published by CRC Press. This book was released on 2020-08-12 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work addresses all of the major topics in Fourier series, emphasizing the concept of approximate identities and presenting applications, particularly in time series analysis. It stresses throughout the idea of homogenous Banach spaces and provides recent results. Techniques from functional analysis and measure theory are utilized.;College and university bookstores may order five or more copies at a special student price, available on request from Marcel Dekker, Inc.
Download or read book Algorithms for Linear Quadratic Optimization written by Vasile Sima and published by CRC Press. This book was released on 1996-03-05 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers theoretical, algorithmic and computational guidelines for solving the most frequently encountered linear-quadratic optimization problems. It provides an overview of recent advances in control and systems theory, numerical line algebra, numerical optimization, scientific computations and software engineering.
Download or read book Global Lorentzian Geometry written by John K. Beem and published by Routledge. This book was released on 2017-09-29 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a neighbourhood of degenerate two-plane, and proof of the Lorentzian Splitting Theorem.;Five or more copies may be ordered by college or university stores at a special student price, available on request.
Download or read book Measure Theory and Integration written by M.M. Rao and published by CRC Press. This book was released on 2018-10-03 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types-providing a complete and detailed review of every aspect of measure and integration theory using valuable examples, exercises, and applications. With more than 170 references for further investigation of the subject, this Second Edition provides more than 60 pages of new information, as well as a new chapter on nonabsolute integrals contains extended discussions on the four basic results of Banach spaces presents an in-depth analysis of the classical integrations with many applications, including integration of nonmeasurable functions, Lebesgue spaces, and their properties details the basic properties and extensions of the Lebesgue-Carathéodory measure theory, as well as the structure and convergence of real measurable functions covers the Stone isomorphism theorem, the lifting theorem, the Daniell method of integration, and capacity theory Measure Theory and Integration, Second Edition is a valuable reference for all pure and applied mathematicians, statisticians, and mathematical analysts, and an outstanding text for all graduate students in these disciplines.
Download or read book Fundamentals of Domination in Graphs written by Teresa W. Haynes and published by CRC Press. This book was released on 1998-01-05 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style. Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination."
Download or read book Prufer Domains written by Marco Fontana and published by CRC Press. This book was released on 1996-09-04 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a picture of the research that has occurred and the techniques that have been involved in studying Prufer domains since about 1970. The text covers generating ideals in Prufer domains, particular overrings of Prufer domains, applications of the theory of overrings, generalized dedekind domains, polynomial extensions and quasi-Prufer domains, and more.
Download or read book Number Theory written by Don Redmond and published by CRC Press. This book was released on 2020-09-29 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a detailed introduction to number theory, demonstrating how other areas of mathematics enter into the study of the properties of natural numbers. It contains problem sets within each section and at the end of each chapter to reinforce essential concepts, and includes up-to-date information on divisibility problems, polynomial congruence, the sums of squares and trigonometric sums.;Five or more copies may be ordered by college or university bookstores at a special price, available on application.
Download or read book Fundamentals of Algebraic Microlocal Analysis written by Goro Kato and published by CRC Press. This book was released on 2020-08-11 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects."
Download or read book Approximation Theory written by Narenda Govil and published by CRC Press. This book was released on 2021-01-31 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."
Download or read book A Unified Signal Algebra Approach to Two Dimensional Parallel Digital Signal Processing written by Louis A. D'Alotto and published by CRC Press. This book was released on 1998-01-09 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to bridge the gap between parallel computer architectures and the creation of parallel digital signal processing (DSP) algorithms. This work offers an approach to digital signal processing utilizing the unified signal algebra environment to develop naturally occurring parallel DSP algorithms.;College or university book shops may order five or more copies at a special student price. Price is available on request.
