Undergraduate Analysis

by Serge Lang

This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, the construction of harmonic functions on the disk, ordinary differential equations, curve integrals, derivatives in vector spaces, multiple integrals, and others. One of the author's main concerns is to achieve a balance between concrete examples and general theorems, augmented by a variety of interesting exercises.

Some new material has been added in this second edition, for example: a new chapter on the global version of integration of locally integrable vector fields; a brief discussion of L^1 - Cauchy sequences, introducing students to the Lebesgue integral; more material on Dirac sequences and families, including a section on the heat kernel; a more systematic discussion of orders of magnitude; and a number of new exercises.

Genres: Mathematics

657 pages, Hardcover

First published January 1, 1983

About the author

Serge Lang was an influential mathematician in the field of number theory. Algebra is his most famous book.

Librarian Note: There is more than one author in the GoodReads database with this name. See this thread for more information.

Reviews

[Pooja · Rating 3 out of 5]

It is good book for maths

[Dan · Rating 2 out of 5]

This was my undergrad real analysis textbook. I don't like real analysis, and I don't like this book. But compared with Rudin's text principles of mathematical analysis it is quite good. If anything this book is not deep enough, but it is a good reference, and I have used it repeatedly since I finished the class.

[Deni Lennon · Rating 5 out of 5]

It is a great book. Straight to the point and includes some topics that other books don´t.
I used through my first class of analysis, and was a great choice.