TY  - BOOK
AU  - Hijab,Omar
ED  - SpringerLink (Online service)
TI  - Introduction to Calculus and Classical Analysis
T2  - Undergraduate Texts in Mathematics,
SN  - 9780387693163
AV  - QA299.6-433 
U1  - 515 23
PY  - 2007///
CY  - New York, NY
PB  - Springer New York
KW  - Global analysis (Mathematics)
KW  - Mathematics
KW  - Analysis
KW  - Real Functions
N1  - The Set of Real Numbers -- Continuity -- Differentiation -- Integration -- Applications
N2  - 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 second 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; * 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; * there are 366 problems. About the first edition: This is a very intriguing, decidedly unusual, and very satisfying treatment of calculus and introductory analysis. It's full of quirky little approaches to standard topics that make one wonder over and over again, "Why is it never done like this?" John Allen Paulos, author of Innumeracy and A Mathematician Reads the Newspaper
UR  - https://doi.org/10.1007/978-0-387-69316-3
ER  -