This is a book written primarily for graduate students and early
researchers in the fields of Analysis and Partial Differential
Equations (PDEs). Coverage of the material is essentially
self-contained, extensive and novel with great attention to details
and rigour. The strength of the book primarily lies in its clear
and detailed explanations, scope and coverage, highlighting and
presenting deep and profound inter-connections between different
related and seemingly unrelated disciplines within classical and
modern mathematics and above all the extensive collection of
examples, worked-out and hinted exercises. There are well over 700
exercises of varying level leading the reader from the basics to
the most advanced levels and frontiers of research. The book can be
used either for independent study or for a year-long graduate level
course. In fact it has its origin in a year-long graduate course
taught by the author in Oxford in 2004-5 and various parts of it in
other institutions later on. A good number of distinguished
researchers and faculty in mathematics worldwide have started their
research career from the course that formed the basis for this
book.
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