Foundations of Mathematical Analysis

by Richard Johnsonbaugh, W.E. Pfaffenberger

This classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. A self-contained text, it presents the necessary background on the limit concept. (The first seven chapters could constitute a one-semester course on introduction to limits.) Subsequent chapters discuss differential calculus of the real line, the Riemann-Stieltjes integral, sequences and series of functions, transcendental functions, inner product spaces and Fourier series, normed linear spaces and the Riesz representation theorem, and the Lebesgue integral. More than 750 exercises help reinforce the material. 1981 edition. 34 figures.

Genres: Mathematics, Textbooks

448 pages, Paperback

First published August 6, 2002

About the author

Richard F. Johnsonbaugh is an American mathematician and computer scientist. His interests include discrete mathematics and the history of mathematics. He is the author of several textbooks.
Johnsonbaugh earned a bachelor's degree in mathematics from Yale University, and then moved to the University of Oregon for graduate study. He completed his Ph.D. at Oregon in 1969. His dissertation, I. Classical Fundamental Groups and Covering Space Theory in the Setting of Cartan and Chevalley; II. Spaces and Algebras of Vector-Valued Differentiable Functions, was supervised by Bertram Yood. He also has a second master's degree in computer science from the University of Illinois at Chicago.
He is currently professor emeritus at De Paul University.

Reviews

[Ben · Rating 4 out of 5]

We used this text book for a functional analysis class I took. It has a pretty good and very rigorous treatment of real and functional analysis. The class mostly focused on metric spaces and this book does a good job covering topics like completeness, Cauchy sequences, compactness, connectnessed, and other topical matter that starts with the letter "C." The latter half of the book covers integration, including the Lebesgue integral, but we did not follow the book's treatment, which is fairly orthodox, of building the Lebesgue integral using measure theory. Instead showed integral must exist as a continuous extension of the Riemann integral using density and completion arguments studied earlier on the book. So, I can not actually comment on the book's treatment of the Lebesgue integral, but I suspect it is done well.

I would like to note that is not an advanced calculus book, as another reviewer described it. At least not in any meaningful sense. Yes it deals with calculus and a lot of the topics covered in a calculus book in a more rigorous fashion, but it is really an advanced real analysis or introductory functional analysis book.

[William Schram · Rating 5 out of 5]

Mathematical Analysis is one of the essential aspects of modern math. The book is a self-contained text on Analysis. It requires a background in Calculus, but the book is easy to understand overall. It defines what each of the symbols means.

The book contains a lot of interesting tidbits. For example, it demonstrates the irrationality of the square root of two.

The book contains problems and exercises to increase understanding. They vary in difficulty from easy to hard. There are hints and solutions to the exercises at the back of the book.

I enjoyed the book. Thanks for reading my review, and see you next time.

[Quadratic Reciprocity · Rating 3 out of 5]

Overall decent and mostly clear exposition, as one should expect with any math book. The main issue for me is that many of the definitions and proofs presented in this book are unmotivated, leaving the reader asking "why did we just do that?!" after each step. Also the graphics are kinda cheesy (I just couldn't convince myself that point on a certain drawing of a parabola looks differentiable!), and the language can get quite stale, unlike Spivak's writing.

[Cora Wang · Rating 5 out of 5]

The bible book

[Scott Neal Reilly · Rating 4 out of 5]

I was looking for something a bit more abstract than this book gave me, but that's more my fault for picking a book from a catalog than flipping through it at a bookstore first. This is a fine advanced calculus college textbook with all the proofs that I recall from my advanced calculus course from days of old. It's clear and well-organized but very proof-based with minimal glue to hold it all together. In this way, it would be a fine class textbook.

[Stephen · Rating 5 out of 5]

This has been such a critical book in my mathematical development. I find myself often referring back to this book as a source to fill in holes, and referring it to colleagues as a good book to do so

[Mills College Library]

515 J719 1981