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Introduction to calculus and classical analysis

Author: O Hijab
Publisher: New York : Springer, ©2007.
Series: Undergraduate texts in mathematics.
Edition/Format:   Print book : English : 2nd edView all editions and formats
Summary:

Involving 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  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: O Hijab
ISBN: 9780387693156 0387693157 9780387693163 0387693165
OCLC Number: 138280218
Description: x, 337 pages : illustrations ; 24 cm
Contents: 1. The set of real numbers. Sets and mappings --
The set R --
The subset N and the principle of induction --
The completeness property --
Sequences and limits --
Nonnegative series and decimal expansions --
Signed series and Cauchy sequences --
2. Continuity. Compactness --
Continuous limits --
Continuous functions --
3. Differentiation. Derivatives --
Mapping properties --
Graphing techniques --
Power series --
Trigonometry --
Primitives --
4. Integration. The Cantor set --
Area --
The integral --
The fundamental theorem of calculus --
The method of exhaustion --
5. Applications. Euler's gamma function --
The number [Greek letter pi] --
Gauss' arithmetic-geometric mean (AGM) --
The Gaussian integral --
Stirling's approximation of n! --
Infinite products --
Jacobi's theta functions --
Riemann's zeta function --
The Euler-Maclaurin formula --
A. Solutions. A.1. Solutions to Chapter 1 --
A.2. Solutions to Chapter 2 --
A.3. Solutions to Chapter 3 --
A.4. Solutions to Chapter 4 --
A.5. Solutions to Chapter 5 --
References --
Index.
Series Title: Undergraduate texts in mathematics.
Responsibility: Omar Hijab.
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