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 all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.

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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 months. This book includes the problems and solutions of the most important mathematical competitions from 2010 to 2014 in China, such as China Mathematical Competition, China Mathematical Olympiad, China Girls' Mathematical Olympiad. These problems are almost exclusively created by the experts who are engaged in mathematical competition teaching and researching. Some of the solutions are from national training team and national team members, their wonderful solutions being the feature of this book. This book is useful to mathematics fans, middle school students engaged in mathematical competition, coaches in mathematics teaching and teachers setting up math elective courses.

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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 in areas such as finite group theory and computer-aided proofs.
* Distills thousands of years of mathematics into a single, approachable volume
* Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present
* Includes up-to-date references and an extensive chronological table of mathematical and general historical developments.
Whether you're interested in the age of Plato and Aristotle or Poincare and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.

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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 alike and their final elaboration as mathematical abstractions, as we know them today, defined in terms of formal logic by means of the idea of a limit of an infinite sequence.
But while the importance of the calculus and mathematical analysis ― the core of modern mathematics ― cannot be overemphasized, the value of this first comprehensive critical history of the calculus goes far beyond the subject matter. This book will fully counteract the impression of laymen, and of many mathematicians, that the great achievements of mathematics were formulated from the beginning in final form. It will give readers a sense of mathematics not as a technique, but as a habit of mind, and serve to bridge the gap between the sciences and the humanities. It will also make abundantly clear the modern understanding of mathematics by showing in detail how the concepts of the calculus gradually changed from the Greek view of the reality and immanence of mathematics to the revised concept of mathematical rigor developed by the great 19th century mathematicians, which held that any premises were valid so long as they were consistent with one another. It will make clear the ideas contributed by Zeno, Plato, Pythagoras, Eudoxus, the Arabic and Scholastic mathematicians, Newton, Leibnitz, Taylor, Descartes, Euler, Lagrange, Cantor, Weierstrass, and many others in the long passage from the Greek "method of exhaustion" and Zeno's paradoxes to the modern concept of the limit independent of sense experience; and illuminate not only the methods of mathematical discovery, but the foundations of mathematical thought as well.

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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 benefit from this book.

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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 linhas e colunas. Áreas e volumes levam ao estudo dos determinantes. Cônicas e quádricas conduzem às formas quadráticas, às matrizes simétricas e seus autovalores.

De um modo geral, o livro mostra como conceitos básicos de Álgebra Linear são úteis para tratar, eficiente e elegantemente, problemas de Geometria Analítica.

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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 finitas e outros, geralmente não discutidos em livros elementares como este, foram incluídos em vista de sua importância nas aplicações e também por servirem de atraentes ilustrações da teoria.

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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.

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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 170 exercícios, agrupados seguindo as seções do livro. Todos esses exercícios acham-se inteiramente resolvidos no capítulo final.

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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. A escolha dos tópicos visou a um equilíbrio entre a estrutura lógica do assunto e a utilidade em possíveis aplicações.

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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 of what is expected of them, what "the game" is, suffer bouts of a kind of mental paralysis. This text attempts to address these problems in several ways: First, we have attempted to define "the game" as that of "inquiry," by using a form of exposition that begins with a question and proceeds to analyze, ultimately to answer it, bringing in definitions, arguments, conjectures, exam­ ples, etc. , as they arise naturally in the course of a narrative discussion of the question. (The true, historical narrative is too convoluted to serve for first explanations, so no attempt at historical accuracy has been made; our narra­ tives are completely contrived. ) Second, we have kept the logic informal, especially in the course of preliminary speculative discussions, where common sense and plausibility­ tempered by mild skepticism-serve to energize the inquiry.

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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, convolutions, Fourier series and the Fourier integral, functions in n-space, derivatives in vector spaces, the inverse and implicit mapping theorem, ordinary differential equations, multiple integrals, and differential forms. My objective is to offer those learning and teaching analysis at the undergraduate level a large number of completed exercises and I hope that this book, which contains over 600 exercises covering the topics mentioned above, will achieve my goal. The exercises are an integral part of Lang's book and I encourage the reader to work through all of them. In some cases, the problems in the beginning chapters are used in later ones, for example, in Chapter IV when one constructs-bump functions, which are used to smooth out singulari­ ties, and prove that the space of functions is dense in the space of regu­ lated maps. The numbering of the problems is as follows. Exercise IX. 5. 7 indicates Exercise 7, §5, of Chapter IX. Acknowledgments I am grateful to Serge Lang for his help and enthusiasm in this project, as well as for teaching me mathematics (and much more) with so much generosity and patience.

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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.

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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, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen­ sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.

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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 discussing recent developments such as the COBE results.

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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

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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 los japoneses bajo las terrazas de templos y santuarios durante la época de aislamiento que Japón tuvo de Occidente. Es común a casi todos los problemas sangaku precisamente el hecho de tratarse de problemas de enunciado sencillo y solución elemental. En algunos pocos casos, sin embargo, la solución del problema era bastante difícil y requería muchos cálculos. Este trabajo comienza presentando una serie de herramientas útiles para resolver con éxito la mayoría de los problemas. Las herramientas básicas son el teorema de Pitágoras y la semejanza de triángulos, aunque también se proporcionan otras menos usuales como los teoremas de Casey y Descartes, entre otros, que serán necesarios para la resolución de algún problema concreto, pero que pueden obviarse en una primera lectura. Preparamos con las herramientas, a continuación están los enunciados de los problemas a resolver. El lector puede echarles un vistazo en general e ir resolviendo los que les parezcan más fáciles, dejando los más difíciles para el final. Se avisa que el orden de los problemas no sigue ningún patrón determinado. Las soluciones de los problemas se incluyen de forma separada a continuación de los enunciados de los problemas. De esta forma nos resulta fácil no ver la solución de un problema si no lo deseamos. Al final, antes de la bibliografía, pueden encontrarse pistas de las soluciones, a las que nos podemos agarrar antes de mirar la solución completa.

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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 definiciones precisa, pacientes explicaciones y problemas cuidadosamente escogidos.

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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 the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra."

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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 1. However, the techniques of Part One are precisely those which are not emphasized in elementary calculus courses, since they are regarded as too sophisticated. The context of a third-year course is the first time that they are given proper emphasis, and thus it is important that Part One be thoroughly mastered. Emphasis has shifted from computational aspects of calculus to theoretical aspects: proofs for theorems concerning continuous 2 functions; sketching curves like x e-X, x log x, xlix which are usually regarded as too difficult for the more elementary courses; and other similar matters.

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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 style meant to engage any reader looking for further insight into mathematics.

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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. Almost every student or scientist, will at some point run into mathematical formulas or ideas in scientific papers that may be hard to understand, given that formal math education may be some years ago.  In this book we will explain the theory behind many of these mathematical ideas and expressions and provide readers with the tools to better understand them. We will revisit high school mathematics and extend and relate this to the mathematics you need to understand the math you may encounter in the course of your research. This book will help you understand the math and formulas in the scientific papers you read. To achieve this goal, each chapter mixes theory with practical pen-and-paper exercises such that you (re)gain experience with solving math problems yourself. Mnemonics will be taught whenever possible. To clarify the math and help readers apply it, each chapter provides real-world and scientific examples.

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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 spacetime and its consequences for Dynamics. The chapter about covariant formulation includes among its topics the concepts of volume and hypersurfaces in manifolds, energy-momentum tensor of a fluid, and prepares the language for General Relativity. The last two chapters are devoted to an introduction of General Relativity and Cosmology in a modern approach connected with the latest discoveries in these areas.

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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 the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun­ dations of calculus (including the "Fundamental Theorem"), and, along the way, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.

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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, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, transfinite induction, the axiom of choice, Zorn’s lemma, empirical induction, and fallacies and induction. He also explains how to write inductive proofs.

The next part contains more than 750 exercises that highlight the levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. Each self-contained chapter in this section includes the necessary definitions, theory, and notation and covers a range of theorems and problems, from fundamental to very specialized.

The final part presents either solutions or hints to the exercises. Slightly longer than what is found in most texts, these solutions provide complete details for every step of the problem-solving process.

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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.

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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 with the forefronts of updated physics and technology.

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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 level, develops the basics, and reinforces fundamentals, ensuring a solid foundation in the principles and methods of physics. It provides an ideal introduction for college-level students of physics, chemistry, and engineering; for motivated AP Physics students; and for general readers interested in advances in the sciences.

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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 revolutionary ideas on relativity and quantum mechanics.

The book begins at the simplest level, develops the basics, and reinforces fundamentals, ensuring a solid foundation in the principles and methods of physics. It provides an ideal introduction for college-level students of physics, chemistry, and engineering, for motivated AP Physics students, and for general readers interested in advances in the sciences.

Instructor resources--including problem sets and sample examinations--and more information about Professor Shankar's course are available at http://oyc.yale.edu/physics/phys-200.

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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 las situaciones, en matemática y en sus aplicaciones, en las que estos objetos están presentes. De ahí la importancia central del Álgebra Lineal en la enseñanza de la matemática. Este libro presenta una exposición introductoria del Álgebra Lineal y no presupone conocimientos anteriores sobre el asunto.

Sin embargo conviene recordar que un curso como éste se ubica de manera natural en el currículo universitario después de un semestre, por lo menos, de Geometría Analítica en dos y tres dimensiones, durante el cual el estudiante debe adquirir alguna familiaridad, a nivel elemental, con la representación algebraica de ideas geométricas y viceversa.

Se ha considerado casi obligatorio, desde hace algunos años, dedicar las primeras sesenta o más páginas de todo libro de Álgebra Lineal al estudio de los sistemas de ecuaciones lineales por el método de la eliminación gaussiana, motivando así la introducción de las matrices y de los determinantes, solo después de eso son definidos los espacios vectoriales.

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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.[...]

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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 restructured to improve the flow of ideas. It now features new examples taken from recent developments, such as laser slowing of atoms, exoplanets and black holes; a 'Hints, Clues and Answers' section for the end-of-chapter problems to support student learning; and a solutions manual for instructors at www.cambridge.org/kandk.

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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 of spectral lines and the ideas of radiation transport. Hydrodynamics begins with the concept of phase-space distribution functions and Boltzmann's equation and develops ideal, viscous and magneto-hydrodynamics all from the vanishing divergence of an energy-momentum tensor, opening a natural extension towards relativistic hydrodynamics. Linear stability analysis is introduced and used as a common and versatile tool throughout the book.

Aimed at students at graduate level, lecturers teaching courses in theoretical astrophysics or advanced topics in modern astronomy, this book with its abundant examples and exercises also serves as a reference and an entry point for more advanced researchers wanting to update their knowledge of the physical processes that govern the behavior and evolution of astronomical objects.

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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 sind sorgfältig aufeinander abgestimmt, beziehen sich aufeinander, verwenden eine möglichst einheitliche Notation und lassen diese vier Gebiete nicht nur jedes für sich entstehen, sondern vermitteln auch einen zusammenhängenden Überblick über die gesamte Grundlage der theoretischen Physik.

Übersichtlich und grafisch ansprechend gegliedert, mit über 500 klaren und verständlichen Abbildungen versehen, bieten alle Kapitel ausführlich vorgerechnete Beispiele, begleitet von insgesamt fast 700 Verständnisfragen, Ausblicken in weiterführende Überlegungen sowie von mehr als 300 Übungsaufgaben mit kommentierten Lösungen.

Der Inhalt des Buchs orientiert sich an den Bachelor- und Masterstudiengängen großer Universitäten in Deutschland, Österreich und der Schweiz und deckt den behandelten Stoff möglichst umfassend ab. Die langjährige und vielfach hervorragend bewertete Lehrerfahrung der Autoren ist hier in einem Buch kondensiert, das Sie nicht nur durch Ihr gesamtes Bachelor-Studium, sondern weit in Ihr Masterstudium hinein begleiten wird.

Dieses Werk wurde ergänzt um mathematische Beiträge der beliebten Bestseller-Autoren Florian Modler und Martin Kreh.

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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 determinants, and finding eigenvectors and eigenvalues. With memorable examples like miniature golf games and karate tournaments, Reiji transforms abstract concepts into something concrete, understandable, and even fun.

As you follow Misa through her linear algebra crash course, you'll learn about:
–Basic vector and matrix operations such as addition, subtraction, and multiplication
–Linear dependence, independence, and bases
–Using Gaussian elimination to calculate inverse matrices
–Subspaces, dimension, and linear span
–Practical applications of linear algebra in fields like computer graphics, cryptography, and engineering

But Misa's brother may get more than he bargained for as sparks start to fly between student and tutor. Will Reiji end up with the girl—or just a pummeling from her oversized brother? Real math, real romance, and real action come together like never before in The Manga Guide to Linear Algebra.

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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 before them. The formalisms are also kept self-contained. Most of the required mathematical tools are also given in the appendices.

Although this book covers all the disciplines of fundamental physics, the book is concise and can be treated as an integrated entity. This is consistent with the aphorism that simplicity is beauty, unification is beauty, and thus physics is beauty. The book may be used as an advanced textbook by graduate students. It is also suitable for physicists who wish to have an overview of fundamental physics.

Contents:

• Basic Principles
• Quantum Fields
• Quantum Fields in Riemann Spacetime
• Symmetry Breaking
• Perturbative Field Theory
• From Quantum Field Theory to Quantum Mechanics
• Electromagnetic Field
• Quantum Mechanics
• Applications of Quantum Mechanics
• Statistical Mechanics
• Applications of Statistical Mechanics
• General Relativity

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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 BACHILLERATO. A PESAR DE LA FAMILIARIDAD CON EL ÁLGEBRA Y LA TRIGONOMETRÍA, SUS HABILIDADES EN ESTAS MATERIAS CON FRECUENCIA SON INSUFICIENTES PARA ALCANZAR EL ÉXITO EN EL CÁLCULO UNIVERSITARIO. CON ESTE TEXTO BUSCAMOS EQUILIBRAR LA ESCASA EXPERIENCIA DE LOS ESTUDIANTES CON EL CÁLCULO Y EL DESARROLLO DE HABILIDADES ALGEBRAICAS QUE PODRÍAN NECESITAR, TODO SIN SOCAVAR O MINAR SU CONFIANZA. ADEMÁS, HEMOS TENIDO CUIDADO DE PRESENTAR SUFICIENTE MATERIAL, SOLUCIONES DETALLADAS PASO A PASO Y EJERCICIOS QUE APOYEN UNA COMPRENSIÓN COMPLETA PARA ALUMNOS DE TODOS LOS NIVELES. ANIMAMOS A LOS ESTUDIANTES A IR MÁS ALLÁ DE LA MEMORIZACIÓN DE LAS FÓRMULAS PARA GENERALIZAR CONCEPTOS CONFORME ÉSTOS SE PRESENTEN. DESPUÉS DE CURSAR CÁLCULO, ELLOS TENGAN CONFIANZA EN SUS HABILIDADES PARA RAZONAR Y RESOLVER PROBLEMAS. EL DOMINIO DEL CÁLCULO CON APLICACIONES PRÁCTICAS AL MUNDO SERÁ SU RECOMPENSA, PERO EL VERDADERO REGALO SERÁ LA HABILIDAD PARA PENSAR Y GENERALIZAR

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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. A PESAR DE LA FAMILIARIDAD CON EL ÁLGEBRA Y LA TRIGONOMETRÍA, SUS HABILIDADES EN ESTAS MATERIAS CON FRECUENCIA SON INSUFICIENTES PARA ALCANZAR EL ÉXITO EN EL CÁLCULO UNIVERSITARIO. CON ESTE TEXTO BUSCAMOS EQUILIBRAR LA ESCASA EXPERIENCIA DE LOS ESTUDIANTES CON EL CÁLCULO Y EL DESARROLLO DE HABILIDADES ALGEBRAICAS QUE PODRÍAN NECESITAR, TODO SIN SOCAVAR O MINAR SU CONFIANZA. ADEMÁS, HEMOS TENIDO CUIDADO DE PRESENTAR SUFICIENTE MATERIAL, SOLUCIONES DETALLADAS PASO A PASO Y EJERCICIOS QUE APOYEN UNA COMPRENSIÓN COMPLETA PARA ALUMNOS DE TODOS LOS NIVELES. ANIMAMOS A LOS ESTUDIANTES A IR MÁS ALLÁ DE LA MEMORIZACIÓN DE LAS FÓRMULAS PARA GENERALIZAR CONCEPTOS CONFORME ÉSTOS SE PRESENTEN. DESPUÉS DE CURSAR CÁLCULO, ELLOS TENGAN CONFIANZA EN SUS HABILIDADES PARA RAZONAR Y RESOLVER PROBLEMAS. EL DOMINIO DEL CÁLCULO CON APLICACIONES PRÁCTICAS AL MUNDO SERÁ SU RECOMPENSA, PERO EL VERDADERO REGALO SERÁ LA HABILIDAD PARA PENSAR Y GENERALIZAR

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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 mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.

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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; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music — and much, much more.

Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.

• Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors
• Presents major ideas and branches of pure mathematics in a clear, accessible style
• Defines and explains important mathematical concepts, methods, theorems, and open problems
• Introduces the language of mathematics and the goals of mathematical research
• Covers number theory, algebra, analysis, geometry, logic, probability, and more
• Traces the history and development of modern mathematics
• Profiles more than ninety-five mathematicians who influenced those working today
• Explores the influence of mathematics on other disciplines
• Includes bibliographies, cross-references, and a comprehensive index

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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 fundamentalmente la Física clásica hasta aquellas que incluyen una cantidad considerable de Física atómica y cuántica. Los diversos tomos pretenden ser compatibles en nivel y estilo de tratamiento, pero en ningún momento se han concebido como una enciclopedia homogénea; por el contrario, cada uno de los libros se han diseñado de modo que sea razonablemente individual en muchos planes de estudio.

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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, together with new sections on applications in science.

Symmetries and invariance principles, the basic geometric aspects of mechanics as well as elements of continuum mechanics also play an important role. The book will enable the reader to develop general principles from which equations of motion follow, to understand the importance of canonical mechanics and of symmetries as a basis for quantum mechanics, and to get practice in using general theoretical concepts and tools that are essential for all branches of physics.

The book contains more than 150 problems with complete solutions, as well as some practical examples which make moderate use of personal computers. This will be appreciated in particular by students using this textbook to accompany lectures on mechanics. The book ends with some historical notes on scientists who made important contributions to the development of mechanics.

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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 from the established Archimedean or Galilean/Huygenian tradition of geometrizing nature?; What is the value of elegance and conciseness?; What is the relation between Newton's geometrical methods and the calculus? This book explains how Newton addressed these issues, taking into consideration the values that directed the research of Newton and his contemporaries. This book will be of interest to researchers and advanced students in departments of history of science, philosophy of science, physics, mathematics and astronomy.

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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 ideas less abstract to students. It explains how various topics in calculus may seem unrelated but in reality have common roots. Emphasizing historical perspectives, the text gives students a glimpse into the development of calculus and its ideas from the age of Newton and Leibniz to the twentieth century. Nearly 300 examples lead to important theorems as well as help students develop the necessary skills to closely examine the theorems. Proofs are also presented in an accessible way to students.

By strengthening skills gained through elementary calculus, this textbook leads students toward mastering calculus techniques. It will help them succeed in their future mathematical or engineering studies.

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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 título puede sugerir, no es solo un magnífico tratado de física matemática, con aportaciones seminales a la teoría de los espacios de Hilbert, sino que también constituye una de las contribuciones más lúcidas al problema del significado físico de la mecánica cuántica, en particular al problema de la medida. Cuestiones como el colapso de la función de ondas, la posibilidad de una versión causal de la teoría cuántica (variables ocultas) o el papel del observador fueron analizadas en estas páginas por John von Neumann con una maestría difícilmente superable, independientemente de que en algún caso (como el de las variables ocultas) sus conclusiones fuesen matizadas más de dos décadas después.

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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 of clear exposition and deep insight.
Timeless and collectible, the lectures are essential reading, not just for students of physics but for anyone seeking an introduction to the field from the inimitable Feynman.

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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 of clear exposition and deep insight.
Timeless and collectible, the lectures are essential reading, not just for students of physics but for anyone seeking an introduction to the field from the inimitable Feynman.

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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 of clear exposition and deep insight.

Timeless and collectible, the lectures are essential reading, not just for students of physics but for anyone seeking an introduction to the field from the inimitable Feynman.

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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 curso al tiempo que añade contenido cuidadosamente revisado. Las pacientes explicaciones, los soberbios ejercicios centrados en la resolución de problemas y las series de ejercicios cuidadosamente graduadas que han hecho de los textos de Stewart best-sellers, continúan proporcionando una base sólida para la séptima edición. De los estudiantes más impreparados a los más talentosos matemáticos, la redacción y la presentación de Stewart sirven para mejorar el entendimiento y fomentar la confianza.

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