Introduction to Calculus and Classical Analysis (Undergraduate Texts in Mathematics) - Hardcover

Hijab, Omar

Hardcover

ISBN 10: 0387949267 ISBN 13: 9780387949260

Publisher: Springer, 1997

Synopsis

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. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by instead using sequences * definition of the integral as the area under the graph, while area is defined for EVERY subset of the plane * complete avoidance of complex numbers * heavy emphasis on computational problems * applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more * 344 problems with solutions in the back of the book

About this title

From the Back Cover

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

Review

Reviews from previous editions:

"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

Edition details

• Publisher: Springer
• Publication date: 1997
• ISBN 10: 0387949267
• ISBN 13: 9780387949260
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 313