This book provides an introduction to the basic ideas and tools used in mathematical analysis.
It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers
topics in both real and complex variables. Considerable space is given to developing Riemann
integration theory in higher dimensions including a rigorous treatment of Fubini's theorem
polar coordinates and the divergence theorem. These are used in the final chapter to derive
Cauchy's formula which is then applied to prove some of the basic properties of analytic
functions. Among the unusual features of this book is the treatment of analytic function theory
as an application of ideas and results in real analysis. For instance Cauchy's integral
formula for analytic functions is derived as an application of the divergence theorem. The last
section of each chapter is devoted to exercises that should be viewed as an integral part of
the text. A Concise Introduction to Analysis should appeal to upper level undergraduate
mathematics students graduate students in fields where mathematics is used as well as to
those wishing to supplement their mathematical education on their own. Wherever possible an
attempt has been made to give interesting examples that demonstrate how the ideas are used and
why it is important to have a rigorous grasp of them.
