Elementary Introduction To The Theory Of Pseudodifferential Operators

Author : Xavier Saint Raymond
ISBN : 9781351452922
Genre : Mathematics
File Size : 76.85 MB
Format : PDF, Kindle

In the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This book provides the fundamental knowledge non-specialists need in order to use microlocal analysis. It is strictly mathematical in the sense that it contains precise definitions, statements of theorems and complete proofs, and follows the usual method of pure mathematics. The book explains the origin of the theory (i.e., Fourier transformation), presents an elementary construcion of distribution theory, and features a careful exposition of standard pseudodifferential theory. Exercises, historical notes, and bibliographical references are included to round out this essential book for mathematics students; engineers, physicists, and mathematicians who use partial differential equations; and advanced mathematics instructors.
Category: Mathematics

Table Of Integrals Series And Products

ISBN : 9781483265643
Genre : Mathematics
File Size : 65.35 MB
Format : PDF

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.
Category: Mathematics

A Treatise On The Theory Of Bessel Functions

Author : G. N. Watson
ISBN : 0521483913
Genre : Mathematics
File Size : 86.28 MB
Format : PDF

This monumental 1995 treatise by the late Professor G. N. Watson wil be indispensable to mathematicians and physicists.
Category: Mathematics

Number Theory

Author : Henri Cohen
ISBN : 9780387498942
Genre : Mathematics
File Size : 37.29 MB
Format : PDF, Mobi

This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject.
Category: Mathematics

Handbook Of Mathematical Functions

Author : Milton Abramowitz
ISBN : 9780486158242
Genre : Mathematics
File Size : 23.39 MB
Format : PDF