This self-contained text, suitable for advanced undergraduates, provides an extensive

introduction to mathematical analysis, from the fundamentals to more advanced

material. It begins with the properties of the real numbers and continues with a rigorous

treatment of sequences, series, metric spaces, and calculus in one variable.

Further subjects include Lebesgue measure and integration on the line, Fourier

analysis, and differential equations. In addition to this core material, the book includes

a number of interesting applications of the subject matter to areas both within

and outside of the field of mathematics. The aim throughout is to strike a balance

between being too austere or too sketchy, and being so detailed as to obscure the essential

ideas. A large number of examples and nearly 500 exercises allow the reader

to test understanding and practice mathematical exposition, and they provide a

window into further topics.

Richard Beals is James E. English Professor of Mathematics at Yale University. He

has also served as a professor at the University of Chicago and as a visiting professor

at the University of Paris, Orsay. He is the author of more than 100 research papers

and monographs in partial differential equations, differential equations, functional

analysis, inverse problems, mathematical physics, mathematical psychology, and

mathematical economics.