SIAM REVIEW "The book succeeds well in providing a sound basis in analysis beyond that which most students will have received as undergraduates...Overall, this text serves as a wonderful introduction to 'useful' analysis for new applied mathematicians."
BULLETIN OF MATHEMATICS BOOKS "This text is written with the usual elegance and orderly style that we have come to expect from this author. Topics are presented in a clear and logical manner, and the text is rich with important and interesting content...This text is well worth considering in any program in applied mathematics, and also by anyone seeking a valuable reference in analysis and its applications."
MATHEMATICAL REVIEWS "The author describes this marvelous book as designed for beginning graduate students in mathematics - in particular for those who intend to specialize in applied mathematics, and for graduate students in other disciplines such as engineering, physics and computer science...Those who are familiar with the author's earlier books will not be surprised by its excellence. It is business-like and will be found to be demanding, but it is user-friendly. It is the reviewer's opinion that it will be extremely useful and popular as a text; institutions that do not already require their students to take such a course no longer have an excuse, and should immediately organize one based on this book...The author gives a rigorous discussion of a very large number of topics. Careful definitions and clearly stated theorems are given...The writing in clear and readable throughout, with a pleasant and friendly style...it is the reviewer's view that the author has presented a rich harvest of useful and interesting analysis in a splendid manner."