A Course in Calculus and Real Analysis

This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for...

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Mathematical Olympiad In China (2011-2014)

The International Mathematical Olympiad (IMO) is a very important competition for high school students. China has taken part in the IMO 31 times since 1985 and has won the top ranking for countries 19 times, with a multitude of gold medals for individual students. The six students China has sent every year were selected from 60 students among approximately 300 students who took part in the annual China Mathematical Competition during the winter...

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A History of Mathematics

The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat s Last Theorem and the Poincare Conjecture, in addition to recent advances...

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The History of the Calculus and Its Conceptual Development

This book, for the first time, provides laymen and mathematicians alike with a detailed picture of the historical development of one of the most momentous achievements of the human intellect ― the calculus. It describes with accuracy and perspective the long development of both the integral and the differential calculus from their early beginnings in antiquity to their final emancipation in the 19th century from both physical and metaphysical ideas...

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Lecture Notes on Newtonian Mechanics

This textbook provides an introduction to classical mechanics at a level intermediate between the typical undergraduate and advanced graduate level. This text describes the background and tools for use in the fields of modern physics, such as quantum mechanics, astrophysics, particle physics, and relativity. Students who have had basic undergraduate classical mechanics or who have a good understanding of the mathematical methods of physics will...

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Geometria Analítica e Algebra Linear

Esta é uma introdução à Geometria Analítica, isto é, ao uso de coordenadas para estudar a Geometria Euclideana – plana e espacial. À medida em que se fazem necessários, os vetores são introduzidos, tirando-se proveito de sua grande simplicidade notacional e seu forte apelo geométrico. Os sistemas lineares são mostrados como um exemplo de conexão da Álgebra com a Geometria, motivando a consideração de matrizes e da dependência linear entre suas...

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Álgebra Linear

É uma introdução à Álgebra Linear, escrita para leitores que não necessitam possuir conhecimentos anteriores sobre o assunto. A apresentação busca um equilíbrio entre a organização teórica da matéria e seus aspectos concretos (ou práticos), como a eliminação gaussiana, o método de Lagrange para diagonalização de formas quadráticas ou as várias decomposições de matrizes. Alguns tópicos, como valores singulares, pseudo-inversa, equações a diferenças...

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Analise Real. Funções de Uma Variável - Volume 3

Este volume completa a trilogia “Análise Real”. Seu subtítulo mantém a tradicional denominação de Análise Vetorial mas o assunto é tratado de forma atualizada, permitindo assim o estudo das integrais de superfície em dimensões superiores. Ele pode ser estudado com proveito pelos leitores com conhecimento equivalente aos conteúdos dos volumes 1 e 2. Como seus antecessores, ele contém as soluções dos exercícios propostos. Downlo...

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Analise Real. Funções de N Variáveis - Volume 2

Este segundo volume da "Análise Real" estuda o Cálculo Diferencial e Integral das funções de n variáveis. Ele é dirigido aos estudantes que possuem conhecimento equivalente ao do primeiro volume, mais noções elementares de Álgebra Linear. O tratamento nele oferecido visa a objetividade, concentrando-se nos pontos relevantes e essenciais, de forma a permitir que a matéria aqui exposta possa ser coberta inteiramente num semestre letivo. São propostos...

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Analise Real. Funções de Uma Variável - Volume 1

Análise Real, volume 1 é uma introdução ao estudo das funções reais de uma variável real, dirigida aos alunos da universidade que já possuam experiência equivalente a um ou dois semestres de Cálculo. A apresentação é elementar, com exemplos ilustrativo s. Praticamente todos os exercícios propostos são resolvidos no capítulo final. O autor preocupou-se em justificar cuidadosamente todas as afirmações feitas, de forma coerente mas sem exageros formais....

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A First Course in Analysis

The first course in Analysis, which follows calculus, along with other courses, such as differential equations and elementary linear algebra, in the curricu­ lum, presents special pedagogical challenges. There is a change of stress from computational manipulation to "proof. " Indeed, the course can become more a course in Logic than one in Analysis. Many students, caught short by a weak command of the means of mathematical discourse and unsure...

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Problems and Solutions for Undergraduate Analysis

The present volume contains all the exercises and their solutions for Lang's second edition of Undergraduate Analysis. The wide variety of exercises, which range from computational to more conceptual and which are of vary­ ing difficulty, cover the following subjects and more: real numbers, limits, continuous functions, differentiation and elementary integration, normed vector spaces, compactness, series, integration in one variable, improper integrals,...

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A First Course in Real Analysis (Undergraduate Texts in Mathematics)

Many changes have been made in this second edition of A First Course in Real Analysis. The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises. The book's readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation. Downlo...

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A First Course in Real Analysis

The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory,...

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The Early Universe (Frontiers in Physics)

The Early Universe has become the standard reference on forefront topics in cosmology, particularly to the early history of the Universe. Subjects covered include primordial nubleosynthesis, baryogenesis, phases transitions, inflation, dark matter, and galaxy formation, relics such as axions, neutrinos and monopoles, and speculations about the Universe at the Planck time. The book includes more than ninety figures as well as a five-page update...

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Apuntes de Teoría de la Medida

Apuntes de Teoría de la Medida Dpto. de Matemáticas Univ. de Extremadura. 27 de mayo de 2016 Descargar...

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Problemas San Gaku o Problemas Bonitos de Geometría resueltos por Métodos Elementales

Se pretende que el título del presente trabajo cumpla dos misiones: Llamar tu la atención. Reflejar el contenido de las páginas que siguen. Esperando que la primera de ellas ya esté conseguida, a partir de aquí comienza a desarrollarse las segunda: conseguir que los problemas y soluciones, así como las técnicas utilizadas te parezcan bonitos e interesantes. Muchos de los problemas aquí presentados son problemas sangaku, es decir problemas que colgaban...

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Cálculo Esencial (Trascendentes Tempranas)

Este libro es para aquellos que piensan que la mayoría de los libros de texto de cálculo son demasiado largos. Al escribir el libro, James Stewart se pregunto: ¿Que es esencial para un curso de cálculo de tres semestres para los científicos e ingenieros? Cálculo Esencial: Trascendentes Tempranas, segunda edición, ofrece un enfoque conciso al cálculo de enseñanza que se centra en los conceptos más importantes, y es compatible con los conceptos con...

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Algebra (Graduate Texts in Mathematics, Band 211)

This book is intended as a basic text for a one year course in algebra at the graduate level or as a useful reference for mathematicians and professionals who use higher-level algebra. This book successfully addresses all of the basic concepts of algebra. For the new edition, the author has added exercises and made numerous corrections to the text. From MathSciNet's review of the first edition: "The author has an impressive knack for presenting...

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Undergraduate Analysis (Undergraduate Texts in Mathematics)

The present volume is a text designed for a first course in analysis. Although it is logically self-contained, it presupposes the mathematical maturity acquired by students who will ordinarily have had two years of calculus. When used in this context, most of the first part can be omitted, or reviewed extremely rapidly, or left to the students to read by themselves. The course can proceed immediately into Part Two after covering Chapters o and...

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Math Talks for Undergraduates

For many years, Serge Lang has given talks on selected items in mathematics which could be extracted at a level understandable by those who have had calculus. Written in a conversational tone, Lang now presents a collection of those talks as a book covering such topics as: prime numbers, the abc conjecture, approximation theorems of analysis, Bruhat-Tits spaces, and harmonic and symmetric polynomials. Each talk is written in a lively and informal...

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Math for Scientists: Refreshing the Essentials

This book reviews math topics relevant to non-mathematics students and scientists, but which they may not have seen or studied for a while. These math issues can range from reading mathematical symbols, to using complex numbers, dealing with equations involved in calculating medication equivalents, the General Linear Model (GLM) used in e.g. neuroimaging analysis, finding the minimum of a function, independent component analysis, or filtering approaches....

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Einstein's Space-Time: An Introduction to Special and General Relativity by Rafael Ferraro (2007-06-07)

Einstein's Space-Time: An Introduction to Special and General Relativity is a textbook addressed to students in physics and other people interested in Relativity and a history of physics. The book contains a complete account of Special Relativity that begins with the historical analysis of the reasons that led to a change in our manner of regarding the space and time. The first chapters are aimed to afford a deep understanding of the relativistic...

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A First Course in Real Analysis

Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to...

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Handbook of Mathematical Induction: Theory and Applications

Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics. In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction,...

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Mathematical Olympiad Challenges

Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory Historical insights and asides are presented to stimulate further inquiry Emphasis is on creative solutions to open-ended problems Many examples, problems and solutions, with a user-friendly and accessible style Enhanced motivatio References. Downlo...

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Physics Olympiad - Basic To Advanced Exercises

This book contains some of the problems and solutions in the past domestic theoretical and experimental competitions in Japan for the International Physics Olympiad. Through the exercises, we aim at introducing the appeal and interest of modern physics to high-school students. In particular, the problems for the second-round of competition are like long journey of physics, beginning with fundamental physics of junior-high-school level, and ending...

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Fundamentals of Physics II: Electromagnetism, Optics, and Quantum Mechanics (The Open Yale Courses Series Book 2)

R. Shankar, a well-known physicist and contagiously enthusiastic educator, was among the first to offer a course through the innovative Open Yale Course program. His popular online video lectures on introductory physics have been viewed over a million times. In this second book based on his online Yale course, Shankar explains essential concepts, including electromagnetism, optics, and quantum mechanics.    The book begins at the simplest...

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Fundamentals of Physics: Mechanics, Relativity, and Thermodynamics (The Open Yale Courses Series)

Professor R. Shankar, a well-known physicist and contagiously enthusiastic educator, was among the first to offer a course through the innovative Open Yale Course program. His popular online video lectures on introductory physics have been viewed over a million times. In this concise and self-contained book based on his online Yale course, Shankar explains the fundamental concepts of physics from Galileo’s and Newton’s discoveries to the twentieth-century’s...

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Álgebra Linear

El Álgebra Lineal es el estudio de los espacios vectoriales y de las transformaciones lineales entre ellos. Cuando los espacios tienen dimensiones finitas, las transformaciones lineales poseen matrices. También poseen matrices las formas bilineales y, más particularmente, las formas cuadráticas. Así el Álgebra Lineal trata con vectores y transformaciones lineales y también con matrices y formas cuadráticas. Son numerosas y bastante variadas...

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Lições De Fisica De Feynman - 3 Volumes

Embalagem com quatro volumes que reúnem o conteúdo das famosas aulas ministradas pelo prof. Feynman a alunos de graduação nos anos de 1962 e 1963 no California Institute of Technology. Esta é uma edição comemorativa aos 100 anos da teoria da relatividade celebrados em 2005. Uma obra primorosa que não pode faltar na biblioteca dos estudiosos e aficionados da área.[...] Downlo...

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An Introduction to Mechanics

For 40 years, Kleppner and Kolenkow's classic text has introduced students to the principles of mechanics. Now brought up to date, this revised and improved second edition is ideal for classical mechanics courses for first- and second-year undergraduates with foundation skills in mathematics. The book retains all the features of the first edition, including numerous worked examples, challenging problems and extensive illustrations, and has been...

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Theoretical Astrophysics: An Introduction

Beginning from first principles and adopting a modular structure, this book develops the fundamental physical methods needed to describe and understand a wide range of seemingly very diverse astrophysical phenomena and processes. For example, the discussion of radiation processes including their spectra is based on Larmor's equation and extended by the photon picture and the internal dynamics of radiating quantum systems, leading to the shapes...

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Theoretische Physik

Die Grundlagen der theoretischen Physik in einem Band – das bietet Ihnen das vorliegende Buch. Sechs in Forschung und Lehre erfahrene Autoren aus Deutschland und Österreich stellen die vier großen Gebiete Mechanik, Elektrodynamik, Quantenmechanik sowie Thermodynamik und Statistische Physik dar. Die besondere Stärke dieses Buches liegt darin, dass es in vielfältigen Querverweisen die inneren Zusammenhänge zwischen diesen Gebieten zeigt. Die Kapitel...

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The Manga Guide to Linear Algebra

Reiji wants two things in life: a black belt in karate and Misa, the girl of his dreams. Luckily, Misa's big brother is the captain of the university karate club and is ready to strike a deal: Reiji can join the club if he tutors Misa in linear algebra. Follow along in The Manga Guide to Linear Algebra as Reiji takes Misa from the absolute basics of this tricky subject through mind-bending operations like performing linear transformations, calculating...

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Principles of Physics ''From Quantum Field Theory to Classical Mechanics''

This book starts from a set of common basic principles to establish the formalisms in all areas of fundamental physics, including quantum field theory, quantum mechanics, statistical mechanics, thermodynamics, general relativity, electromagnetic field, and classical mechanics. Instead of the traditional pedagogic way, the author arranges the subjects and formalisms in a logical-sequential way, i.e. all the formulas are derived from the formulas...

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Cálculo De Varias Variables (12ª ED.)

ESTA NUEVA EDICIÓN OFRECE UNA INTRODUCCIÓN MODERNA AL CÁLCULO QUE APOYA LA COMPRENSIÓN CONCEPTUAL, PERO CONSERVA LOS ELEMENTOS ESENCIALES DE UN CURSO TRADICIONAL. TALES MEJORAS SE RELACIONAN ESTRECHAMENTE CON UNA VERSIÓN AMPLIADA DEL TEXTO DE MYMATHLAB®, EL CUAL BRINDA APOYO ADICIONAL A LOS ESTUDIANTES Y FLEXIBILIDAD A LOS PROFESORES. MUCHOS ALUMNOS ESTUVIERON EXPUESTOS A LA TERMINOLOGÍA Y LOS ASPECTOS COMPUTACIONALES DEL CÁLCULO DURANTE EL...

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Cálculo De Una Variable (12ª ED.)

ESTA NUEVA EDICIÓN OFRECE UNA INTRODUCCIÓN MODERNA AL CÁLCULO QUE APOYA LA COMPRENSIÓN CONCEPTUAL, PERO CONSERVA LOS ELEMENTOS ESENCIALES DE UN CURSO TRADICIONAL. TALES MEJORAS SE RELACIONAN ESTRECHAMENTE CON UNA VERSIÓN AMPLIADA DEL TEXTO DE MYMATHLAB®, EL CUAL BRINDA APOYO ADICIONAL A LOS ESTUDIANTES Y FLEXIBILIDAD A LOS PROFESORES. MUCHOS ALUMNOS ESTUVIERON EXPUESTOS A LA TERMINOLOGÍA Y LOS ASPECTOS COMPUTACIONALES DEL CÁLCULO DURANTE EL BACHILLERATO....

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Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled  “On the Number of Prime Numbers Less Than a Given Quantity.”  Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it. Alternating passages of extraordinarily lucid...

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The Princeton Companion to Mathematics

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world’s leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics;...

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Relatividad Especial

Esta serie de Introducción a la Física del M.I.T., una producción directa del trabajo del Centro, está destinada a ser un conjunto de textos que globalmente abarquen las áreas principales de la Física básica. La serie pretende destacar la interacción de la experiencia y la intuición en el desarrollo de las teorías físicas. Los libros de la misma proporcionan una variedad de bases posibles para los cursos de introducción, desde aquellas que destacan...

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Mechanics: From Newton's Laws to Deterministic Chaos

This book covers all topics in mechanics from elementary Newtonian mechanics, the principles of canonical mechanics and rigid body mechanics to relativistic mechanics and nonlinear dynamics. It was among the first textbooks to include dynamical systems and deterministic chaos in due detail. As compared to the previous editions the present 6th edition is updated and revised with more explanations, additional examples and problems with solutions,...

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Reading The Principia

Isaac Newton's Principia is considered one of the masterpieces in the history of science. The mathematical methods employed by Newton in the Principia stimulated much debate among his contemporaries, especially Leibniz, Huygens, Bernoulli and Euler, who debated their merits and drawbacks. Among the questions they asked were: How should natural philosophy be mathematized?; Is it legitimate to use uninterpreted symbols?; Is it possible to depart...

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Advanced Calculus

Suitable for a one- or two-semester course, Advanced Calculus: Theory and Practice expands on the material covered in elementary calculus and presents this material in a rigorous manner. The text improves students’ problem-solving and proof-writing skills, familiarizes them with the historical development of calculus concepts, and helps them understand the connections among different topics. The book takes a motivating approach that makes...

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Fundamentos Matemáticos De La Mecánica Cuántica

Publicado en alemán en 1932, Fundamentos matemáticos de la mecánica cuántica (1932), del polivalente matemático húngaro John von Neumann (1903-1957), uno de los cerebros más poderosos del siglo XX, contiene la presentación matemáticas más acabada y rigurosa de la mecánica cuántica, desarrollada en 1925-1926 por Werner Heisenberg, Erwing Schrödinger y Paul Dirac. Es todo un clásico de la literatura científica. Pero, al contrario de lo que su...

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Lectures On Physics Vol III

"The whole thing was basically an experiment," Richard Feynman said late in his career, looking back on the origins of his lectures. The experiment turned out to be hugely successful, spawning publications that have remained definitive and introductory to physics for decades. Ranging from the basic principles of Newtonian physics through such formidable theories as general relativity and quantum mechanics, Feynman's lectures stand as a monument...

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Lectures On Physics Vol II

"The whole thing was basically an experiment," Richard Feynman said late in his career, looking back on the origins of his lectures. The experiment turned out to be hugely successful, spawning publications that have remained definitive and introductory to physics for decades. Ranging from the basic principles of Newtonian physics through such formidable theories as general relativity and quantum mechanics, Feynman's lectures stand as a monument...

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Lectures On Physics Vol I

"The whole thing was basically an experiment," Richard Feynman said late in his career, looking back on the origins of his lectures. The experiment turned out to be hugely successful, spawning publications that have remained definitive and introductory to physics for decades. Ranging from the basic principles of Newtonian physics through such formidable theories as general relativity and quantum mechanics, Feynman's lectures stand as a monument...

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Cálculo De Una Variable

Cálculo de una variable, Trascendentes tempranas es ampliamente reconocido por su precisión matemática y la exactitud, claridad de la exposición y notables ejemplos y conjuntos de problemas. Millones de estudiantes en todo el mundo han estudiado el cálculo a través del estilo registrado de Stewart, mientras que los instructores han adoptado su planteamiento una y otra vez. En la séptima edición, Stewart continúa estableciendo el estándar para el...

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