Analysis: From Concepts to Applications (Universitext)

December 8, 2020
Analysis: From Concepts to Applications (Universitext)

Presents results of analysis that can be applied to a wealth ofconcrete problemsStarts from the foundations and leads to powerful resultsTreats less traditional topics such as convex analysis,monotone operators, and the Laplace and Radon transforms——————————This textbook covers the main results and methods of realanalysis in a single volume. Taking a progressive approach toequations and transformations, this book starts with the veryfoundations of real analysis (set theory, order, convergence, andmeasure theory) before presenting powerful results that can beapplied to concrete problems.In addition to classical results of functional analysis,differential calculus and integration, Analysis discussestopics such as convex analysis, dissipative operators andsemigroups which are often absent from classical treatises.Acknowledging that analysis has significantly contributed to theunderstanding and development of the present world, the bookfurther elaborates on techniques which pervade modern civilization,including wavelets in information theory, the Radon transform inmedical imaging and partial differential equations in variousmechanical and physical phenomena.Advanced undergraduate and graduate students, engineers as wellas practitioners wishing to familiarise themselves with conceptsand applications of analysis will find this book useful. With itscontent split into several topics of interest, the book’s style andlayout make it suitable for use in several courses, while itsself-contained character makes it appropriate for self-study.