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: The text is completely self-contained and starts with the real number axioms; There is a heavy emphasis on computational problems; There are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta 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; There are 385 problems with all the solutions at the back of the text.

Approaches calculus and introductory analysis in a nonstandard way New edition extensively revised and updated Completely self-contained text Includes supplementary material: sn.pub/extras

Autorentext

Omar Hijab is Professor of Mathematics and Associate Dean for Faculty Affairs, Information Technology, and Operations in the College of Science and Technology at Temple University. He received his Ph.D. in Mathematics from the University of California, Berkeley, and has served previously as Chair of the Department of Mathematics at Temple University. His research interests include systems theory and control; probability theory and stochastic processes; differential equations; mathematical physics; and optimization.

Inhalt
Preface.- 1 The Set of Real Numbers.- 2 Continuity.- 3 Differentiation.- 4 Integration.- 5 Applications.- A Solutions.- References.- Index