A Radical Approach to Real Analysis (Classroom Resource Materials) - Tapa blanda

Bressoud, David

 
9780883857014: A Radical Approach to Real Analysis (Classroom Resource Materials)
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ISBN 10: 0883857014 ISBN 13: 9780883857014
Editorial: The Mathematical Association of America, 1996

Sinopsis

This book is an undergraduate introduction to real analysis. Teachers can use it as a textbook for an innovative course, or as a resource for a traditional course. Students who have been through a traditional course, but do not understand what real analysis is about and why it was created, will find answers to many of their questions in this book. Although this is not a history of analysis, the author returns to the roots of the subject to make it more comprehensible. The book begins with Fourier's introduction of trigonometric series and the problems they created for the mathematicians of the early nineteenth century. Cauchy's attempts to establish a firm foundation for calculus follow, and the author considers his failures and his successes. The book culminates with Dirichlet's proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet's proof. Mathematica ® commands and programs are included in the exercises. However, the reader may use any mathematical tool that has graphing capabilities, including the graphing calculator.

"Sinopsis" puede pertenecer a otra edición de este libro.

Críticas

'What is radical about this book as real analysis books go, is its stronger historical approach ... The past decade or so has witnessed the appearance of a substantial number of 'bridge the gap' introductions to real analysis which lead the students at a gentler pace through the fundamentals of real analysis according to the traditional syllabus. It is well worth considering whether students in their first undergraduate real analysis course might be better served by a radical approach such as Bressoud's.' Mathematical Reviews

Reseña del editor

This book is an undergraduate introduction to real analysis. Teachers can use it as a textbook for an innovative course, or as a resource for a traditional course. Students who have been through a traditional course, but do not understand what real analysis is about and why it was created, will find answers to many of their questions in this book. Although this is not a history of analysis, the author returns to the roots of the subject to make it more comprehensible. The book begins with Fourier's introduction of trigonometric series and the problems they created for the mathematicians of the early nineteenth century. Cauchy's attempts to establish a firm foundation for calculus follow, and the author considers his failures and his successes. The book culminates with Dirichlet's proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet's proof. Mathematica ® commands and programs are included in the exercises. However, the reader may use any mathematical tool that has graphing capabilities, including the graphing calculator.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
The Mathematical Association of America
Año de publicación
1996
Idioma
Inglés
ISBN 10 
0883857014
ISBN 13 
9780883857014
Encuadernación
Tapa blanda
Número de páginas
336
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

9780883857472: A Radical Approach to Real Analysis 2nd Edition Hardback (Mathematical Association of America Textbooks)

Edición Destacada

ISBN 10:  0883857472 ISBN 13:  9780883857472
Editorial: The Mathematical Association of ..., 2007
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