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9781441924094

Taschenbuch

342

Omar Hijab

533 g

235x155x mm

Undergraduate Texts in Mathematics

Englisch

2nd editionInvolving rigorous analysis, computational dexterity, and a breadth of applications, this book is ideal for undergraduate majors. For this second edition, the author has corrected errors, rewritten large portions of the text, and has introduced new topics.

The Set of Real Numbers.- Continuity.- Differentiation.- Integration.- Applications.- Solutions.- References.- Index.

Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: complete avoidance of /epsilon-/delta arguments by using sequences instead 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. 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

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

2nd editionInvolving rigorous analysis, computational dexterity, and a breadth of applications, this book is ideal for undergraduate majors. For this second edition, the author has corrected errors, rewritten large portions of the text, and has introduced new topics.

The Set of Real Numbers.- Continuity.- Differentiation.- Integration.- Applications.- Solutions.- References.- Index.

Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: complete avoidance of /epsilon-/delta arguments by using sequences instead 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. 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

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

Autor: Omar Hijab

ISBN-13:: 9781441924094

ISBN: 1441924094

Verlag: Springer, Berlin

Gewicht: 533g

Seiten: 342

Sprache: Englisch

Auflage 2nd ed.

Sonstiges: Taschenbuch, 235x155x mm, 65 SW-Abb.

ISBN-13:: 9781441924094

ISBN: 1441924094

Verlag: Springer, Berlin

Gewicht: 533g

Seiten: 342

Sprache: Englisch

Auflage 2nd ed.

Sonstiges: Taschenbuch, 235x155x mm, 65 SW-Abb.