Functional Analysis: A First Course Pdf

Authors: Geveci, Tunc
Carefully dissects key concepts such as limits of sequence, convergence & divergence of monotone sequences, infinite limits, derivatives, integrals, and series of real numbers
Contextualizes subtle, commonly-misunderstood topics such as the notion of an infinite limit, the ε-δ definitions (for a better command of uniform versus pointwise continuity), error in local linear approximations, and integrability criteria
Includes more than 120 exercises, with a solution manual available to instructors

Authors: DiBenedetto, Emmanuele

The main focus of this textbook, in two parts, is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. The exposition moves systematically from the basic to more sophisticated concepts with recent developments and several open problems. With challenging exercises, examples, and illustrations to help explain the rigorous analytic basis for the Navier–-Stokes equations, mean curvature flow equations, and other important equations describing real phenomena, this book is written for graduate students and researchers, not only in mathematics but also in other disciplines.

Authors: Loeb, Peter A
Written by one of the leading scholars in the field Includes a novel presentation of differentiation and absolute continuity using a local maximum function, resulting in an exposition that is both simpler and more general than the traditional approach
Theorems are stated for Lebesgue and Borel measures, with a note indicating when the same proof works only for Lebesgue measures
Appendices cover additional material, including theorems for higher dimensions and a short introduction to nonstandard analysis