Author	Pรณlya, George. author
Title	Problems and Theorems in Analysis I [electronic resource] : Series. Integral Calculus. Theory of Functions / by George Pรณlya, Gabor Szegรถ
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1998
Connect to	http://dx.doi.org/10.1007/978-3-642-61983-0
Descript	XIX, 393 p. online resource

From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems. These volumes contain many extraordinary problems and sequences of problems, mostly from some time past, well worth attention today and tomorrow. Written in the early twenties by two young mathematicians of outstanding talent, taste, breadth, perception, perseverence, and pedagogical skill, this work broke new ground in the teaching of mathematics and how to do mathematical research. (Bulletin of the American Mathematical Society)

One Infinite Series and Infinite Sequences -- 1 Operations with Power Series -- 2 Linear Transformations of Series. A Theorem of Cesร ro -- 3 The Structure of Real Sequences and Series -- 4 Miscellaneous Problems -- Two Integration -- 1 The Integral as the Limit of a Sum of Rectangles -- 2 Inequalities -- 3 Some Properties of Real Functions -- 4 Various Types of Equidistribution -- 5 Functions of Large Numbers -- Three Functions of One Complex Variable. General Part -- 1 Complex Numbers and Number Sequences -- 2 Mappings and Vector Fields -- 3 Some Geometrical Aspects of Complex Variables -- 4 Cauchyโ{128}{153}s Theorem โ{128}ข The Argument Principle -- 5 Sequences of Analytic Functions -- 6 The Maximum Principle -- Author Index