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1. Fundamentals of real analysis [1998]
 Berberian, Sterling K., 1926
 New York : Springer, 1998.
 Description
 Book — xi, 479 p. ; ill. ; 24 cm.
 Summary

 Foundations. Lebesgue Measure. Topology. Lebesgue Integral. Differentiation. Function Spaces. Product Measure. The Differential Equation y'= f(x, y). Topics in Measure and Integration.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA300 .B4574 1998  Unknown 
2. A first course in real analysis [1994]
 Berberian, Sterling K., 1926
 New York : SpringerVerlag, c1994.
 Description
 Book — xi, 237 p. : ill. ; 25 cm.
 Summary

 1: Axioms for the Field (R) of Real Numbers.
 2: First Properties of (R).
 3: Sequences of Real Numbers, Convergence.
 4: Special Subsets of (R).
 5: Continuity.
 6: Continuous Functions on an Interval.
 7: Limits of Functions.
 8: Derivatives.
 9: Riemann Integral.
 10: Infinite Series.
 11: Beyond the Riemann Integral.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
The book offers an initiation into mathematical reasoning, and into the mathematician's mindset and reflexes. Specifically, the fundamental operations of calculusdifferentiation and integration of functions and the summation of infinite seriesare 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.
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA300 .B457 1994  Unknown 