A First Course in Real Analysis (Undergraduate Texts in Mathematics) - Tapa blanda

Berberian, Sterling K. K.

 
9781461264330: A First Course in Real Analysis (Undergraduate Texts in Mathematics)
Tapa blanda
ISBN 10: 1461264332 ISBN 13: 9781461264330
Editorial: Springer, 2012

Sinopsis

The book offers an initiation into mathematical reasoning, and into the mathematician's mind-set and reflexes. Specifically, the fundamental operations of calculus--differentiation and integration of functions and the summation of infinite series--are built, with logical continuity (i.e., "rigor"), starting from the real number system.

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

Reseña del editor

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.

Reseña del editor

The book offers an initiation into mathematical reasoning, and into the mathematician's mind-set and reflexes. Specifically, the fundamental operations of calculus--differentiation and integration of functions and the summation of infinite series--are built, with logical continuity (i.e., "rigor"), starting from the real number system. The first chapter sets down precise axioms for the real number system, from which all else is derived using the logical tools summarized in an Appendix. The discussion of the "fundamental theorem of calculus," the focal point of the book, especially thorough. The concluding chapter establishes a significant beachhead in the theory of the Lebesgue integral by elementary means.

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

Editorial
Springer
Año de publicación
2012
Idioma
Inglés
ISBN 10 
1461264332
ISBN 13 
9781461264330
Encuadernación
Tapa blanda
Número de páginas
256
Contacto del fabricante
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Alemania

Otras ediciones populares con el mismo título

9781493991044: First Course In Real Analysis

Edición Destacada

ISBN 10:  1493991043 ISBN 13:  9781493991044
Editorial: SPRINGER, 2019
Tapa blanda