This second edition is a corrected, revised, and reprinted version of our original textbook. We are particularly grateful to readers who have sent in suggestions for corrections. Among them we owe a huge debt to R. B. Burckel (Kansas State University). Many of his corrections and suggestions are incorporated in this new edition. Thanks too to Keith Yates (Manchester Metropolitan University) who, while working on some of the more difficult problems, found some further errors.
In teaching first courses in real analysis over the years, we have found increasingly that the classes form rather heterogeneous groups. It is no longer true that most of the students are first-year graduate students in mathematics, presenting more or less common backgrounds for the course. Indeed, nowadays we find diverse backgrounds and diverse objectives among students in such classes. Some students are undergraduates, others are more advanced. Many students are in other departments, such as statistics …
The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.
This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context.
However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it …
This book is a one semester course in basic analysis. It started its life as my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in Fall semester 2009.
Later I added the metric space chapter to teach Math 521 at University of Wisconsin–Madison (UW). A prerequisite for this course is a basic proof course, using for example [H], [F], or [DW]. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school (such as UIUC 444), but also as a more advanced one-semester course that also covers topics such as metric spaces (such as UW 521).
It should also be possible to run a faster course without metric spaces covering all sections of chapters 0 through 6. The approximate number of lectures given in the section notes through chapter 6 are a very rough estimate and were designed for the slower course. The first few chapters of the book can be used in an introductory …
This edition differs from the original 2001 version only in that we corrected a number of misprints and other errors. We are grateful to the many users of that version for notifying us of errors they found. We would like to make special mention of Richard Delaware (University of Missouri-Kansas City), and Steve Agronsky (California State Polytechnic University, San Luis Obispo), both of whom went through the entire first edition, made many helpful suggestions, and found numerous errors.
University mathematics departments have for many years offered courses with titles such as Advanced Calculus or Introductory Real Analysis. These courses are taken by a variety of students, serve a number of purposes, and are written at various levels of sophistication. The students range from ones who have just completed a course in elementary calculus to beginning graduate students in mathematics. The purposes are multifold:
- To present familiar concepts from calculus at a more …
MATLAB es un paquete de software que se utiliza principalmente en el campo de la ingeniería para el procesamiento de señales, análisis de datos numéricos, modelos, programación, simulación y visualización gráfica del equipo.
En los últimos años, ha llegado a ser ampliamente aceptado como una herramienta eficiente y, por lo tanto, su uso se ha incrementado significativamente en las comunidades científicas e instituciones académicas.
Este libro consta de 20 capítulos los cuales representan diversos trabajos de investigación vanguardista que utilizan como herramienta base MATLAB. Estos capítulos incluyen técnicas para la programación y desarrollo de Interfaces Gráficas de Usuario (GUI), sistemas dinámicos, máquinas eléctricas, señales y procesamiento de imágenes, electrónica de potencia, circuitos de señal mixta, programación genética, marcas de agua digitales, sistemas de control de series de tiempo de modelado de regresión y neuronales …
Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves.
This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational …
This text is an outgrowth of lectures given at the University of Windsor, Canada. One of our main objectives is updating the undergraduate analysis as a rigorous postcalculus course. While such excellent books as Dieudonn´e's Foundations of Modern Analysis are addressed mainly to graduate students, we try to simplify the modern Bourbaki approach to make it accessible to sufficiently advanced undergraduates.
On the other hand, we endeavor not to lose contact with classical texts, still widely in use. Thus, unlike Dieudonn´e, we retain the classical notion of a derivative as a number (or vector), not a linear transformation. Linear maps are reserved for later (Volume II) to give a modern version of differentials. Nor do we downgrade the classical mean-value theorems or Riemann–Stieltjes integration, but we treat the latter rigorously in Volume II, inside Lebesgue theory. First, however, we present the modern Bourbaki theory of antidifferentiation, adapted to an undergraduate…
This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course.
The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a
Numerical Analysis - Theory and Application es un libro dividido en dos partes: una primera dedicada a la teoría, y una segunda más práctica dedicada al enfoque de lo expuesto en la anterior.
El objetivo de este texto es el planteamiento teórico de los distintos métodos de análisis numéricos, así como de sus aplicaciones en la resolución de los problemas tanto en esta teoría de números como en el campo de la ingeniería.
Dado que un gran número de investigaciones teóricas puras se orientan a la búsqueda de resultados a través de simulaciones numéricas, este libro puede ser útil tanto para la investigación más formal como para la aplicada.
Foundation's Math Analysis is a rigorous text that takes students from analyzing functions to mathematical induction to an introduction to calculus.
Table of Contents
- Analyzing Functions
- Analyzing Polynomial and Rational Functions
- Analyzing Exponential and Logarithmic Functions
- Polar Equations and Complex Numbers
- Analyzing Conic Sections
- Sequences, Series, and Mathematical Induction
- Introduction to Calculus