000			01263nam a22001937a 4500
020			_a9781493991044
082			_a515 _bBER/F
100			_aBerberian,Sterling K
245			_aA first course in real analysis/ _cSterling K Berberian
260			_aNew York: _b Springer-Verlag, _c1994.
300			_axi,237p.
490			_aUndergraduate texts in mathematics.
500			_aIncludes bibliographical refernces and Index.
520			_aThe 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.
650			_aMathematical Analysis
650			_aNumbers- _vReal
650			_aMathematics
942			_cBK
999			_c613618 _d613618