Introduction to Calculus and Classical Analysis

Abstract

This text is intended for an honors calculus course or for an introductionto analysis. Involving rigorous analysis, computational dexterity,and a breadth of applications, it is ideal for undergraduate majors.This third edition includes corrections as well as some additionalmaterial.Some features of the text:* The text is completely self-contained and starts with the real numberaxioms;* The integral is defined as the area under the graph, while the areais defined for every subset of the plane;* There is a heavy emphasis on computational problems, from the high-schoolquadratic formula to the formula for the derivative of the zeta functionat zero;* There are applications from many parts of analysis, e.g., convexity,the Cantor set, continued fractions, the AGM, the theta and zetafunctions, transcendental numbers, the Bessel and gamma functions,and many more;* Traditionally transcendentally presented material, such as infiniteproducts, the Bernoulli series, and the zeta functional equation,is developed over the reals;* There are 385 problems with all the solutions at the back of thetext.Review from the first edition:"This is a very intriguing, decidedly unusual, and very satisfyingtreatment of calculus and introductory analysis. It's full of quirkylittle approaches to standard topics that make one wonder over andover again, 'Why is it never done like this?'"-John Allen Paulos, author of Innumeracy and A Mathematician Readsthe Newspaper