Preface Objectives of This Book * To teach calculus as a laboratory science, with the computer and software as the lab, and to use this lab as an essential tool in learning and using calculus.
Starting with Cook's pioneering work on NP-completeness in 1970, polynomial complexity theory, the study of polynomial-time com- putability, has quickly emerged as the new foundation of algorithms.
This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis.
For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis.
Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as the dimension tends to infinity.
Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions.
Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives.
Inequalities based on Sobolev Representations deals exclusively with very general tight integral inequalities of Chebyshev-Gruss, Ostrowski types and of integral means, all of which depend upon the Sobolev integral representations of functions.
On February 15-17, 1993, a conference on Large Scale Optimization, hosted by the Center for Applied Optimization, was held at the University of Florida.
This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par- tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in Ankara, Turkey, sponsored by The Scientific and Tech- nical Research Council of Turkey and the Middle East Technical University.
This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSN097) which was held in Ischia, Italy, in June 1997.
This monograph represents a summary of our work in the last two years in applying the method of simulated annealing to the solution of problems that arise in the physical design of VLSI circuits.
The principal aim in writing this book has been to provide an intro- duction, barely more, to some aspects of Fourier series and related topics in which a liberal use is made of modem techniques and which guides the reader toward some of the problems of current interest in harmonic analysis generally.
This Student Guide is exceptional, maybe even unique, among such guides in that its author, Fred Soon, was actually a student user of the textbook during one of the years we were writing and debugging the book.
This book considers methods of approximate analysis of mechanical, elec- tromechanical, and other systems described by ordinary differential equa- tions.
Mathematics students generally meet the Riemann integral early in their undergraduate studies, then at advanced undergraduate or graduate level they receive a course on measure and integration dealing with the Lebesgue theory.
From the reviews: "e;A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics.
Broadly speaking, analysis is the study of limiting processes such as sum- ming infinite series and differentiating and integrating functions, and in any of these processes there are two issues to consider; first, there is the question of whether or not the limit exists, and second, assuming that it does, there is the problem of finding its numerical value.
Assuming only calculus and linear algebra, this book introduces the reader in a technically complete way to measure theory and probability, discrete martingales, and weak convergence.
