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, including:

• 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 - 344 problems with solutions in the back of the book - interesting applications, many of which are not usually found in advanced calculus books.

For this second 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.

Klappentext

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.

Inhalt

The Set of Real Numbers.- Continuity.- Differentiation.- Integration.- Applications.