Synopses & Reviews
This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. The book contains many remarkable features: - complete avoidance of /epsilon-/delta arguments by instead using sequences, - definition of the integral as the area under the graph, while area is defined for EVERY subset of the plane, - complete avoidance of complex numbers, - heavy emphasis on computational problems, - applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more, - 344 problems with solutions in the back of the book, - interesting applications, many of which are not usually found in advanced calculus books
About the first edition:
"The treatment, however, is far from standard, and many topics are included, especially in the last chapter, that are not available in other modern elementary texts...This is a rigorous book with good motivational material and explanatory remarks. It includes 347 problems, with solutions given in a 73-page appendix...some of the most attractive material requires considerable skill in manipulation." D.H. Armitage (MathSciNet).
New in the second edition:
For the new edition, the author has corrected errors and rewritten large portions of the text. In addition, the author has introduced new topics, such as a combinatorial proof that the radius of convergence of the Bernoulli series is 2p.
"ICCA is beautifully conceived and carefully executed...[this book] has much to teach, both about mathematics and how to write mathematics." Marvin Knopp, American Mathematical Monthly.
Synopsis
Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by using sequences instead * definition of the integral as the area under the graph, while area is defined for every subset of the plane * complete avoidance of complex numbers * heavy emphasis on computational problems * applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more * 344 problems with solutions in the back of the book.
Synopsis
Involving rigorous analysis, computational dexterity, and a breadth of applications, this book is ideal for undergraduate majors. For this second edition, the author has corrected errors, rewritten large portions of the text, and has introduced new topics.
Table of Contents
The Set of Real Numbers.- Continuity.- Differentiation.- Integration.- Applications.- Solutions.- References.- Index.