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A first course in real analysis / Sterling K. Berberian.

By: Material type: TextTextSeries: Undergraduate texts in mathematicsNew York : Springer-Verlag, c1994Description: xi, 237 pages : illustrations ; 25 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 9781461264330
  • 0387942173
  • 3540942173
Subject(s): DDC classification:
  • 515.8 20
LOC classification:
  • QA300 .B457 1994
Online resources:
Contents:
Content: Ch. 1. Axioms for the Field R of Real Numbers Ch. 2. First Properties of R Ch. 3. Sequences of Real Numbers, Convergence Ch. 4. Special Subsets of R Ch. 5. Continuity Ch. 6. Continuous Functions on an Interval Ch. 7. Limits of Functions Ch. 8. Derivatives Ch. 9. Riemann Integral Ch. 10. Infinite Series Ch. 11. Beyond the Riemann Integral.
Summary: Summary: "This 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". - Author
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Holdings
Item type Current library Collection Call number Status Notes Date due Barcode
2 Hour Special Reserve 2 Hour Special Reserve Matheson Library Special Reserve - 2 Hours Use items Special Reserve SR 515.8 B484 (Browse shelf(Opens below)) Available Recommended text for MC 163246

"With 19 illustrations"

Includes bibliographical references and indexes.

Content:
Ch. 1. Axioms for the Field R of Real Numbers
Ch. 2. First Properties of R
Ch. 3. Sequences of Real Numbers, Convergence
Ch. 4. Special Subsets of R
Ch. 5. Continuity
Ch. 6. Continuous Functions on an Interval
Ch. 7. Limits of Functions
Ch. 8. Derivatives
Ch. 9. Riemann Integral
Ch. 10. Infinite Series
Ch. 11. Beyond the Riemann Integral.

Summary:
"This 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". - Author

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