Finite Differences Calculus

This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory.

This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere.

This collection covers all fields of mathematics, a must-have for the aspiring maths students and scholars alike.

This is the largest collection I've ever seen, I have not seen it around for a while so I am reseeding it.

1. Purpose The purpose of this work is to provide, in one volume, a wide spectrum of essential (non-measure theoretic) Mathematics for use by workers in the variety of applied fields. To obtain the background developed here in one volume would require studying a prohibitive number of separate Mathematics courses (assuming they were available). Before, much of the material now covered was (a) unavailable, (b) too widely scattered, or © too advanced as presented, to be of use to those who need it. Here, we present a sound basis requiring only Calculus through however, Differential Equations. It provides the needed flexibility to cope, in a rigorous manner, with the every-day, non-standard and new situations that present themselves.

A First Course in Partial Differential Equations: with Complex Variables and Transform Methods

by H. F. Weinberger

ISBN: 048668640X
Dover Publications


Text presents the general properties of partial differential equations such as characteristics, domains of independence and maximum principles. Solutions.