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A Short Book on Long Sums: Infinite Series for Calculus Students

Posted By: AvaxGenius
Date: 9 Dec 2023 05:51:39
A Short Book on Long Sums: Infinite Series for Calculus Students

A Short Book on Long Sums: Infinite Series for Calculus Students by Fernando Q. Gouvêa
English | PDF EPUB (True) | 2023 | 153 Pages | ISBN : 3031375564 | 13 MB

This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series—and infinite series in general—are a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural.
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Fundamentals of Real Analysis

Posted By: AvaxGenius
Date: 15 Nov 2023 08:02:22
Fundamentals of Real Analysis

Fundamentals of Real Analysis by Sterling K. Berberian
English | PDF | 1999 | 492 Pages | ISBN : 0387984801 | 87.3 MB

Integration theory and general topology form the core of this textbook for a first-year graduate course in real analysis. After the foundational material in the first chapter (construction of the reals, cardinal and ordinal numbers, Zorn's lemma and transfinite induction), measure, integral and topology are introduced and developed as recurrent themes of increasing depth. The treatment of integration theory is quite complete (including the convergence theorems, product measure,
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Nonstandard Analysis in Practice

Posted By: AvaxGenius
Date: 2 Nov 2023 15:44:07
Nonstandard Analysis in Practice

Nonstandard Analysis in Practice by Francine Diener, Marc Diener
English | PDF | 1995 | 262 Pages | ISBN : 3540602976 | 34.3 MB

The purpose of this book is to provide an effective introduction to nonstandard methods. A short tutorial giving the necessary background, is followed by applications to various domains, independent from each other. These include complex dynamical systems, stochastic differential equations, smooth and algebraic curves, measure theory, the external calculus, with some applications to probability. The authors have been using Nonstandard Analysis for many years in their research. They all belong to the growing nonstandard school founded by G. Reeb, which is attracting international and interdisciplinary interest.
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Multivariate Birkhoff Interpolation

Posted By: AvaxGenius
Date: 23 Aug 2023 15:14:07
Multivariate Birkhoff Interpolation

Multivariate Birkhoff Interpolation by Rudolph A. Lorentz
English | PDF | 1992 | 200 Pages | ISBN : 3540558705 | 14.1 MB

The subject of this book is Lagrange, Hermite and Birkhoff (lacunary Hermite) interpolation by multivariate algebraic polynomials. It unifies and extends a new algorithmic approach to this subject which was introduced and developed by G.G. Lorentz and the author. One particularly interesting feature of this algorithmic approach is that it obviates the necessity of finding a formula for the Vandermonde determinant of a multivariate interpolation in order to determine its regularity (which formulas are practically unknown anyways) by determining the regularity through simple geometric manipulations in the Euclidean space. Although interpolation is a classical problem, it is surprising how little is known about its basic properties in the multivariate case. The book therefore starts by exploring its fundamental properties and its limitations.
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Analysis I: Convergence, Elementary functions

Posted By: AvaxGenius
Date: 29 Jul 2023 18:40:28
Analysis I: Convergence, Elementary functions

Analysis I: Convergence, Elementary functions by Roger Godement
English | PDF | 2004 | 453 Pages | ISBN : 3540059237 | 42.6 MB

Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.
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Examples and Theorems in Analysis

Posted By: AvaxGenius
Date: 29 Jul 2023 15:35:25
Examples and Theorems in Analysis

Examples and Theorems in Analysis by Peter Leslie Walker
English | PDF | 2004 | 292 Pages | ISBN : 1852334932 | 19.1 MB

Examples and Theorems in Analysis takes a unique and very practical approach to mathematical analysis. It makes the subject more accessible by giving the examples equal status with the theorems. The results are introduced and motivated by reference to examples which illustrate their use, and further examples then show how far the assumptions may be relaxed before the result fails.
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Short Calculus: The Original Edition of “A First Course in Calculus”

Posted By: AvaxGenius
Date: 10 Jun 2023 11:54:59
Short Calculus: The Original Edition of “A First Course in Calculus”

Short Calculus: The Original Edition of “A First Course in Calculus” by Serge Lang
English | PDF (True) | 2002 | 276 Pages | ISBN : 0387953272 | 15 MB

Praise for the first edition:
"..Lang's present book is a source of interesting ideas and brilliant techniques." Acta Scientiarum Mathematicarum
"..It is an admirable straightforward introduction to calculus." Mathematika
This is a reprint of A First Course in Calculus, which has gone through five editions since the early sixties. It covers all the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. As sociological and educational conditions have evolved in various ways over the past four decades, it has been found worthwhile to make the original edition available again. The audience consists of those taking the first calculus course, in high school or college. The approach is the one which was successful decades ago, involving clarity, and adjusted to a time when the students' background was not as substantial as it might be. We are now back to those times, so its time to start over again.
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Large Scale Optimization: State of the Art

Posted By: AvaxGenius
Date: 7 May 2023 15:20:26
Large Scale Optimization: State of the Art

Large Scale Optimization: State of the Art by W. W. Hager, D. W. Hearn, P. M. Pardalos
English | PDF | 1994 | 470 Pages | ISBN : 0792327985 | 37.8 MB

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. The con­ ference was supported by the National Science Foundation, the U. S. Army Research Office, and the University of Florida, with endorsements from SIAM, MPS, ORSA and IMACS. Forty one invited speakers presented papers on mathematical program­ ming and optimal control topics with an emphasis on algorithm development, real world applications and numerical results. Participants from Canada, Japan, Sweden, The Netherlands, Germany, Belgium, Greece, and Denmark gave the meeting an important international component. At­ tendees also included representatives from IBM, American Airlines, US Air, United Parcel Serice, AT & T Bell Labs, Thinking Machines, Army High Performance Com­ puting Research Center, and Argonne National Laboratory.
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Integral Geometry and Convolution Equations (Repost)

Posted By: AvaxGenius
Date: 22 Mar 2023 18:13:59
Integral Geometry and Convolution Equations (Repost)

Integral Geometry and Convolution Equations by V. V. Volchkov
English | PDF | 2003 | 466 Pages | ISBN : 140201628X | 3.85 MB

Integral geometry deals with the problem of determining functions by their integrals over given families of sets. These integrals de?ne the corresponding integraltransformandoneofthemainquestionsinintegralgeometryaskswhen this transform is injective.
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Banach Lattices

Posted By: AvaxGenius
Date: 15 Feb 2023 17:21:50
Banach Lattices

Banach Lattices by Peter Meyer-Nieberg
English | PDF | 1991 | 407 Pages | ISBN : 3540542019 | 50.3 MB

This book is concerned primarily with the theory of Banach lattices and with linear operators defined on, or with values in, Banach lattices. More general classes of Riesz spaces are considered so long as this does not lead to more complicated constructions or proofs. The intentions for writing this book were twofold. First, there appeared in the literature many results completing the theory extensively.
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Fourier Series: A Modern Introduction Volume 1

Posted By: AvaxGenius
Date: 24 Dec 2022 03:59:23
Fourier Series: A Modern Introduction Volume 1

Fourier Series: A Modern Introduction Volume 1 by R. E. Edwards
English | PDF | 1979 | 230 Pages | ISBN : 0387904123 | 17 MB

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. The use of modem concepts and techniques is, in fact, as wide­ spread as is deemed to be compatible with the desire that the book shall be useful to senior undergraduates and beginning graduate students, for whom it may perhaps serve as preparation for Rudin's Harmonic Analysis on Groups and the promised second volume of Hewitt and Ross's Abstract Harmonic Analysis.
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Calculus II

Posted By: AvaxGenius
Date: 20 Nov 2022 04:00:40
Calculus II

Calculus II by Jerrold Marsden, Alan Weinstein
English | PDF | 1985 | 361 Pages | ISBN : 0387909753 | 29 MB

The goal of this text is to help students leam to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition. We list below some of the key features of the book. Examples and Exercises The exercise sets have been carefully constructed to be of maximum use to the students. With few exceptions we adhere to the following policies.
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Calculus III

Posted By: AvaxGenius
Date: 20 Nov 2022 01:10:46
Calculus III

Calculus III by Jerrold Marsden, Alan Weinstein
English | PDF | 1985 | 359 Pages | ISBN : 0387909850 | 37.4 MB

The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition. We list below some of the key features of the book. Examples and Exercises The exercise sets have been carefully constructed to be of maximum use to the students. With few exceptions we adhere to the following policies .
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Several Real Variables

Posted By: AvaxGenius
Date: 16 Nov 2022 17:01:42
Several Real Variables

Several Real Variables by Shmuel Kantorovitz
English | PDF | 2016 | 315 Pages | ISBN : 3319279556 | 3.2 MB

This undergraduate textbook is based on lectures given by the author on the differential and integral calculus of functions of several real variables. The book has a modern approach and includes topics such as:
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Mathematical Analysis: Linear and Metric Structures and Continuity (Repost)

Posted By: AvaxGenius
Date: 27 Oct 2022 11:38:12
Mathematical Analysis: Linear and Metric Structures and Continuity (Repost)

Mathematical Analysis: Linear and Metric Structures and Continuity by Mariano Giaquinta, Giuseppe Modica
English | PDF | 2007 | 475 Pages | ISBN : 0817643745 | 32.5 MB

This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces.
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