2011-04-06 | ISBN: 1441994874 | PDF | 364 Pages | 5.64 MB
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. This third edition includes??? corrections as well as some additional material.
Some features of the text include: The text is completely self-contained and starts with the real number??? axioms; The integral is defined as the area under the graph, while the area is??? defined for every subset of the plane; There is a heavy emphasis on computational problems, from the high-school??? quadratic formula to the formula for the derivative of the zeta function at??? zero; There are applications from many parts of analysis, e.g., convexity, the??? Cantor set, continued fractions, the AGM, the theta and zeta functions,??? transcendental numbers, the Bessel and gamma functions, and many more; Traditionally transcendentally presented material, such as infinite??? products, the Bernoulli series, and the zeta functional equation, is developed??? over the reals; and There are 385 problems with all the solutions at the back of the text.