@article{726465,
      note = {Includes index.},
      author = {Godement, Roger, and Ray, Urmie,},
      url = {http://library.usi.edu/record/726465},
      title = {Analysis., III,: Analytic and differential functions,  manifolds and Riemann surfaces [electronic resource] /},
      abstract = {Volume III sets out classical Cauchy theory. It is much  more geared towards its innumerable applications than  towards a more or less complete theory of analytic  functions. Cauchy-type curvilinear integrals are then shown  to generalize to any number of real variables (differential  forms, Stokes-type formulas). The fundamentals of the  theory of manifolds are then presented, mainly to provide  the reader with a "canonical'' language and with some  important theorems (change of variables in integration,  differential equations). A final chapter shows how these  theorems can be used to construct the compact Riemann  surface of an algebraic function, a subject that is rarely  addressed in the general literature though it only requires  elementary techniques. Besides the Lebesgue integral,  Volume IV will set out a piece of specialized mathematics  towards which the entire content of the previous volumes  will converge: Jacobi, Riemann, Dedekind series and  infinite products, elliptic functions, classical theory of  modular functions and its modern version using the  structure of the Lie algebra of SL(2,R).},
      doi = {https://doi.org/10.1007/978-3-319-16053-5},
      recid = {726465},
      pages = {1 online resource (vii, 321 pages) :},
}