The Resource Introduction to Calculus and Classical Analysis, by Omar Hijab, (electronic resource)

Introduction to Calculus and Classical Analysis, by Omar Hijab, (electronic resource)

Label
Introduction to Calculus and Classical Analysis
Title
Introduction to Calculus and Classical Analysis
Statement of responsibility
by Omar Hijab
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
This completely self-contained text is intended either for a course in honors calculus or for an introduction to analysis. Beginning with the real number axioms, and involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate math majors. This fourth edition includes an additional chapter on the fundamental theorems in their full Lebesgue generality, based on the Sunrise Lemma. Key features of this text include: ⢠Applications from several 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; ⢠A heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; ⢠Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; ⢠A self-contained treatment of the fundamental theorems of calculus in the general case using the Sunrise Lemma; ⢠The integral is defined as the area under the graph, while the area is defined for every subset of the plane; ⢠450 problems with all the solutions presented at the back of the text. Reviews: "Chapter 5 isâ¦an astonishing tour de forceâ¦" âSteven G. Krantz, American Math. Monthly "For a treatmentâ¦[of infinite products and Bernoulli series] that is very close to Eulerâs and even more elementaryâ¦" âV. S. Varadarajan, Bulletin AMS "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?'" âJohn Allen Paulos, Author of Innumeracy and A Mathematician Reads the Newspaper
Member of
http://library.link/vocab/creatorName
Hijab, O
Image bit depth
0
LC call number
QA401-425
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
Undergraduate Texts in Mathematics,
http://library.link/vocab/subjectName
  • Mathematics
  • Approximation theory
  • Sequences (Mathematics)
  • Functions, Special
  • Combinatorial analysis
  • Mathematics
  • Approximations and Expansions
  • Sequences, Series, Summability
  • Special Functions
  • Combinatorics
Label
Introduction to Calculus and Classical Analysis, by Omar Hijab, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Preface -- A Note to the Reader -- 1. The Set of Real Numbers -- 2. Continuity -- 3. Differentiation.-4. Integration -- 5. Applications -- 6. Generalizations -- A. Solutions -- References -- Index
Dimensions
unknown
Edition
4th ed. 2016.
Extent
XIII, 427 p. 69 illus., 1 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783319284002
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-28400-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-28400-2
Label
Introduction to Calculus and Classical Analysis, by Omar Hijab, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Preface -- A Note to the Reader -- 1. The Set of Real Numbers -- 2. Continuity -- 3. Differentiation.-4. Integration -- 5. Applications -- 6. Generalizations -- A. Solutions -- References -- Index
Dimensions
unknown
Edition
4th ed. 2016.
Extent
XIII, 427 p. 69 illus., 1 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783319284002
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-28400-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-28400-2

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