Introduction to Calculus and Classical Analysis

Description

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. Front Matter....Pages i-xiii The Set of Real Numbers....Pages 1-47 Continuity....Pages 49-72 Differentiation....Pages 73-129 Integration....Pages 131-191 Applications....Pages 193-275 Generalizations....Pages 277-313 Back Matter....Pages 315-427