000			02720cam a2200325 i 4500
999			_c3683 _d3683
003			OSt
005			20210811120301.0
008			130211m20139999enk b 001 0 eng
020			_a9781107032033 (hardback)
020			_a9781107675322 (paperback)
040			_aDLC _cKABLIB _dKABLIB
042			_apcc
082	0	0	_a514.325 _223 _bGAR
100	1		_aGarling, D. J. H. _93879
245	1	0	_aA course in mathematical analysis / _cD. J. H. Garling.
264		1	_aCambridge : _bCambridge University Press, _c2013.
300			_a617 p . : _c26 cm
336			_atext _2rdacontent
337			_aunmediated _2rdamedia
338			_avolume _2rdacarrier
504			_aIncludes bibliographical references and index.
505	1		_av. 2. Metric and topological spaces, functions of a vector variable
505	8		_aMachine generated contents note: Introduction; Part I. Metric and Topological Spaces: 1. Metric spaces and normed spaces; 2. Convergence, continuity and topology; 3. Topological spaces; 4. Completeness; 5. Compactness; 6. Connectedness; Part II. Functions of a Vector Variable: 7. Differentiating functions of a vector variable; 8. Integrating functions of several variables; 9. Differential manifolds in Euclidean space; Appendix A. Linear algebra; Appendix B. Quaternions; Appendix C. Tychonoff's theorem; Index.
520			_a"The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume I focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables: differentiation is developed in a co-ordinate free way, while integration (the Riemann integral) is established for functions defined on subsets of Euclidean space. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume III covers complex analysis and the theory of measure and integration. "-- _cProvided by publisher.
650		0	_aMetric spaces. _99797
650		0	_aTopological spaces. _99798
650		0	_aVector valued functions. _99799
650		7	_aMATHEMATICS / Mathematical Analysis. _2bisacsh _93881
942			_2ddc _cBOOK