A Primer of Real Functions

Front Cover
Ralph P. Boas, Harold P. Boas
Cambridge University Press, 1996 - Mathematics - 305 pages
1 Review
This is a revised, updated, and augmented edition of a classic Carus monograph with a new chapter on integration and its applications. Earlier editions covered sets, metric spaces, continuous functions, and differentiable functions. To that, this edition adds sections on measurable sets and functions and the Lebesgue and Stieltjes integrals. The book retains the informal chatty style of the previous editions. It presents a variety of interesting topics, many of which are not commonly encountered in undergraduate textbooks, such as the existence of continuous everywhere-oscillating functions; two functions having equal derivatives, yet not differing by a constant; application of Stieltjes integration to the speed of convergence of infinite series. For readers with a background in calculus, the book is suitable either for self-study or for supplemental reading in a course on advanced calculus or real analysis. Students of mathematics will find here the sense of wonder that was associated with the subject in its early days.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Sets
1
Sets of real numbers
5
Countable and uncountable sets
8
Metric spaces
21
Open and closed sets
25
Dense and nowhere dense sets
38
Compactness
45
Convergence and completeness
52
Approximations to continuous functions
126
Linear functions
132
Derivatives
139
Monotonic functions
158
Convex functions
175
Infinitely differentiable functions
186
Integration
195
Measurable functions
201

Nested sets and Baires theorem
61
Some applications of Baires Theorem
66
Sets of measure zero
73
Functions
77
Continuous functions
83
Properties of continuous functions
90
Upper and lower limits
105
Sequences of functions
108
Uniform convergence
112
Pointwise limits of continuous functions
123
Definition of the Lebesgue integral
206
Properties of Lebesgue integrals
211
Applications of the Lebesgue integral
217
Stieltjes integrals
224
Applications of the Stieltjes integral
229
Partial sums of infinite series
237
Answers to Exercises
245
Index
281
Copyright

Common terms and phrases

References to this book

Advanced Mathematical Thinking
David Tall
No preview available - 1994
All Book Search results »

About the author (1996)

Harold P. Boas received his PhD from MIT in 1980. Between 1980 and 1984 he was J. F. Ritt Assistant Professor of Mathematics at Columbia University. Since 1984 he has been on the faculty at Texas A & M University. He has served as book-review editor of The American Mathematical Monthly (1998 1999) and as editor of the Notices of the American Mathematical Society (2001 2003). In 1995, he and his collaborator Emil J. Straube received the Stefan Bergman Prize from the American Mathematical Society for their research on the boundary regularity theory of the multidimensional inhomogeneous Cauchy-Riemann equations. The Mathematical Association of America has recognized him for an outstanding expository article with the Lester R. Ford Award (2007) and the Chauvenet Prize (2009). He received the Student Led Award for Teaching Excellence from Texas A & M University in 2009. He previously revised his father's A Primer of Real Functions (fourth edition, 1996).

Bibliographic information