000			02184 a2200265 4500
003			IN-KoSCC
005			20241214110848.0
008			210819b xxu||||| |||| 00| 0 eng d
020			_a9789388347730 _cRs. 325.00
040			_cIIT Kanpur
041			_aeng
082			_a515.9 _bK96Pa
100	1	0	_aKumaresan, S.
245	1	2	_aA pathway to complex anaysis _cS. Kumaresan
260			_bTechno World _c2021 _aKolkata
300			_avii, 283 p.
520			_aThis book is an honest attempt to establish a long-cherished belief that Complex Analysis is a fine meeting ground of analysis, geometry and topology. In the last five decades the curriculum has improved a lot and students in India have an exposure to real analysis, linear algebra, metric spaces and topology. Keeping the improved background of the students in mind, we develop the subject. The salient features of this book are: A careful treatment of argument and logarithms. Use of triangles and piecewise smooth paths in place of rectifiable paths. Geometric treatments of C-R equations, winding numbers and fractional linear transformations. A geometric treatment of analytic continuation explaining the subtleties to the beginner. The treatment of conformal property of holomorphic functions using the notion of oriented angles. Many insightful remarks which give a wider perspective to the readers and show them the `big picture'. We emphasize the central point of the Cauchy theory, viz., the existence of local primitives and that of the local power series expansion. We point out how the properties of the holomorphic functions are the local/global manifestations of the corresponding results for power series. Many students approach the subject "Complex Analysis" with a sense of wonder, mystery and awe. They are mystified by the infinite differentiability of `analytic’ functions and so-called multivalued functions. The book will demystify them.
650			_aFunctions of complex variables
650			_aMathematical analysis
650			_aMathematics—Complex numbers
650			_aAnalytic functions
650			_aMathematical analysis
650			_aAdvanced mathematics
942			_cBK _2ddc _n0
999			_c41564 _d41564