This textbook covers the main results and methods of real analysis in a single volume. Taking a
progressive approach to equations and transformations this book starts with the very
foundations of real analysis (set theory order convergence and measure theory) before
presenting powerful results that can be applied to concrete problems. In addition to classical
results of functional analysis differential calculus and integration Analysis discusses
topics such as convex analysis dissipative operators and semigroups which are often absent
from classical treatises. Acknowledging that analysis has significantly contributed to the
understanding and development of the present world the book further elaborates on techniques
which pervade modern civilization including wavelets in information theory the Radon
transform in medical imaging and partial differential equations in various mechanical and
physical phenomena. Advanced undergraduate and graduate students engineers as well as
practitioners wishing to familiarise themselves with concepts and applications of analysis will
find this book useful. With its content split into several topics of interest the book's style
and layout make it suitable for use in several courses while its self-contained character
makes it appropriate for self-study.
