MARC details
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06904cam a2200373 a 4500 |
| 001 - CONTROL NUMBER |
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14888888 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20170828113706.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
070612s2008 njua b 001 0 eng |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER |
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| LC control number |
2007024690 |
| 015 ## - NATIONAL BIBLIOGRAPHY NUMBER |
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| National bibliography number |
GBA787064 |
| Source |
bnb |
| 016 7# - NATIONAL BIBLIOGRAPHIC AGENCY CONTROL NUMBER |
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| Record control number |
014200662 |
| Source |
Uk |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9788126542376 |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)ocn144770075 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
DLC |
| Transcribing agency |
DLC |
| Modifying agency |
BAKER |
| -- |
BTCTA |
| -- |
YDXCP |
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UKM |
| -- |
C#P |
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IXA |
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GZT |
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NOR |
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DLC |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA300 |
| Item number |
.S376 2008 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515 |
| Edition number |
22 |
| Item number |
SCH-M |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Schroder, Bernd S. W. |
| 245 10 - TITLE STATEMENT |
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| Title |
Mathematical analysis : |
| Remainder of title |
a concise introduction |
| Statement of responsibility, etc |
Bernd S.W. Schroder. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
|---|
| Place of publication, distribution, etc |
Hoboken, N.J. : |
| Name of publisher, distributor, etc |
Wiley, |
| Date of publication, distribution, etc |
c2008. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xv, 562 p. : |
| Other physical details |
ill. ; |
| Dimensions |
25 cm. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references (p. 551-552) and index. |
| 505 00 - FORMATTED CONTENTS NOTE |
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| Title |
Table of contents -- |
| -- |
Preface -- |
| Miscellaneous information |
pt. 1. |
| Title |
Analysis of functions of a single real variable -- |
| Miscellaneous information |
1. |
| Title |
The real numbers -- |
| Miscellaneous information |
1.1. |
| Title |
Field axioms -- |
| Miscellaneous information |
1.2. |
| Title |
Order axioms -- |
| Miscellaneous information |
1.3. |
| Title |
Lowest upper and greatest lower bounds -- |
| Miscellaneous information |
1.4. |
| Title |
Natural numbers, integers, and rational numbers -- |
| Miscellaneous information |
1.5. |
| Title |
Recursion, induction, summations, and products -- |
| Miscellaneous information |
2. |
| Title |
Sequences of real numbers -- |
| Miscellaneous information |
2.1. |
| Title |
Limits -- |
| Miscellaneous information |
2.2. |
| Title |
Limit laws -- |
| Miscellaneous information |
2.3. |
| Title |
Cauchy sequences -- |
| Miscellaneous information |
2.4. |
| Title |
Bounded sequences -- |
| Miscellaneous information |
2.5. |
| Title |
Infinite limits -- |
| Miscellaneous information |
3. |
| Title |
Continuous functions -- |
| Miscellaneous information |
3.1. |
| Title |
Limits of functions -- |
| Miscellaneous information |
3.2. |
| Title |
Limit laws -- |
| Miscellaneous information |
3.3. |
| Title |
One-sided limits and infinite limits -- |
| Miscellaneous information |
3.4. |
| Title |
Continuity -- |
| Miscellaneous information |
3.5. |
| Title |
Properties of continuous functions -- |
| Miscellaneous information |
3.6. |
| Title |
Limits at infinity -- |
| Miscellaneous information |
4. |
| Title |
Differentiable functions -- |
| Miscellaneous information |
4.1. |
| Title |
Differentiability -- |
| Miscellaneous information |
4.2. |
| Title |
Differentiation rules -- |
| Miscellaneous information |
4.3. |
| Title |
Rolle's theorem and the mean value theorem -- |
| Miscellaneous information |
5. |
| Title |
The Riemann integral 1 -- |
| Miscellaneous information |
5.1. |
| Title |
Riemann sums and the integral -- |
| Miscellaneous information |
5.2. |
| Title |
Uniform continuity and integrability of continuous functions -- |
| Miscellaneous information |
5.3. |
| Title |
The fundamental theorem of calculus -- |
| Miscellaneous information |
5.4. |
| Title |
The Darboux integral -- |
| 505 00 - FORMATTED CONTENTS NOTE |
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| Miscellaneous information |
6. |
| Title |
Series of real numbers 1 -- |
| Miscellaneous information |
6.1. |
| Title |
Series as a vehicle to define infinite sums -- |
| Miscellaneous information |
6.2. |
| Title |
Absolute convergence and unconditional convergence -- |
| Miscellaneous information |
7. |
| Title |
Some set theory -- |
| Miscellaneous information |
7.1. |
| Title |
The algebra of sets -- |
| Miscellaneous information |
7.2. |
| Title |
Countable sets -- |
| Miscellaneous information |
7.3. |
| Title |
Uncountable sets -- |
| Miscellaneous information |
8. |
| Title |
The Riemann integral 2 -- |
| Miscellaneous information |
8.1. |
| Title |
Outer Lebesgue measure -- |
| Miscellaneous information |
8.2. |
| Title |
Lebesgue's criterion for Riemann integrability -- |
| Miscellaneous information |
8.3. |
| Title |
More integral theorems -- |
| Miscellaneous information |
8.4. |
| Title |
Improper Riemann integrals -- |
| Miscellaneous information |
9. |
| Title |
The Lebesgue integral -- |
| Miscellaneous information |
9.1. |
| Title |
Outer Lebesgue measure -- |
| Miscellaneous information |
9.2. |
| Title |
Lebesgue measurable sets -- |
| Miscellaneous information |
9.2. |
| Title |
Lebesgue measurable functions -- |
| Miscellaneous information |
9.3. |
| Title |
Lebesgue integration -- |
| Miscellaneous information |
9.4. |
| Title |
Lebesgue integrals versus Riemann integrals-- |
| Miscellaneous information |
10. |
| Title |
Series of real numbers 2 -- |
| Miscellaneous information |
10.1. |
| Title |
Limits superior and inferior -- |
| Miscellaneous information |
10.2. |
| Title |
The root test and the ratio test -- |
| Miscellaneous information |
10.3. |
| Title |
Power series -- |
| Miscellaneous information |
11. |
| Title |
Sequences of functions -- |
| Miscellaneous information |
11.1. |
| Title |
Notions of convergence -- |
| Miscellaneous information |
11.2. |
| Title |
Uniform convergence -- |
| Miscellaneous information |
12. |
| Title |
Transcendental functions -- |
| Miscellaneous information |
12.1. |
| Title |
The exponential function -- |
| Miscellaneous information |
12.2. |
| Title |
Sine and cosine -- |
| Miscellaneous information |
12.3. |
| Title |
L'Hôpital's rule -- |
| Miscellaneous information |
13. |
| Title |
Numerical methods -- |
| Miscellaneous information |
13.1. |
| Title |
Approximation with Taylor polynomials -- |
| Miscellaneous information |
13.2. |
| Title |
Newton's method -- |
| Miscellaneous information |
13.3. |
| Title |
Numerical integration -- |
| 505 00 - FORMATTED CONTENTS NOTE |
|---|
| Miscellaneous information |
pt. 2. |
| Title |
Analysis in abstract spaces -- |
| Miscellaneous information |
14. |
| Title |
Integration on measure spaces -- |
| Miscellaneous information |
14.1. |
| Title |
Measure spaces -- |
| Miscellaneous information |
14.2. |
| Title |
Outer measures -- |
| Miscellaneous information |
14.3. |
| Title |
Measurable functions -- |
| Miscellaneous information |
14.4. |
| Title |
Integration of measurable functions -- |
| Miscellaneous information |
14.5. |
| Title |
Monotone and dominated convergence -- |
| Miscellaneous information |
14.6. |
| Title |
Convergence in mean, in measure, and almost everywhere -- |
| Miscellaneous information |
14.7. |
| Title |
Product [sigma]-algebras -- |
| Miscellaneous information |
14.8. |
| Title |
Product measures and Fubini's theorem -- |
| Miscellaneous information |
15. |
| Title |
The abstract venues for analysis -- |
| Miscellaneous information |
15.1. |
| Title |
Abstraction 1 : Vector spaces -- |
| Miscellaneous information |
15.2. |
| Title |
Representation of elements : bases and dimension -- |
| Miscellaneous information |
15.3. |
| Title |
Identification of spaces : isomorphism -- |
| Miscellaneous information |
15.4. |
| Title |
Abstraction 2 : inner product spaces -- |
| Miscellaneous information |
15.5. |
| Title |
Nicer representations : orthonormal sets -- |
| Miscellaneous information |
15.6. |
| Title |
Abstraction 3 : normed spaces -- |
| Miscellaneous information |
15.7. |
| Title |
Abstraction 4 : metric spaces -- |
| Miscellaneous information |
15.8. |
| Title |
L[superscript]p spaces -- |
| Miscellaneous information |
15.9. |
| Title |
Another number field : complex numbers -- |
| Miscellaneous information |
16. |
| Title |
The topology of metric spaces -- |
| Miscellaneous information |
16.1. |
| Title |
Convergence of sequences -- |
| Miscellaneous information |
16.2. |
| Title |
Completeness -- |
| Miscellaneous information |
16.3. |
| Title |
Continuous functions -- |
| Miscellaneous information |
16.4. |
| Title |
Open and closed sets -- |
| Miscellaneous information |
16.5. |
| Title |
Compactness -- |
| Miscellaneous information |
16.6. |
| Title |
The normed topology of R[superscript]d -- |
| Miscellaneous information |
16.7. |
| Title |
Dense subspaces -- |
| Miscellaneous information |
16.8. |
| Title |
Connectedness -- |
| Miscellaneous information |
16.9. |
| Title |
Locally compact spaces -- |
| 505 00 - FORMATTED CONTENTS NOTE |
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| Miscellaneous information |
17. |
| Title |
Differentiation in normed spaces -- |
| Miscellaneous information |
17.1. |
| Title |
Continuous linear functions -- |
| Miscellaneous information |
17.2. |
| Title |
Matrix representation of linear functions -- |
| Miscellaneous information |
17.3. |
| Title |
Differentiability -- |
| Miscellaneous information |
17.4. |
| Title |
The mean value theorem -- |
| Miscellaneous information |
17.5. |
| Title |
How partial derivatives fit in -- |
| Miscellaneous information |
17.6. |
| Title |
Multilinear functions (tensors) -- |
| Miscellaneous information |
17.7. |
| Title |
Higher derivatives -- |
| Miscellaneous information |
17.8. |
| Title |
The implicit function theorem -- |
| Miscellaneous information |
18. |
| Title |
Measure, topology and differentiation -- |
| Miscellaneous information |
18.1. |
| Title |
Lebesgue measurable sets in R[superscript]d -- |
| Miscellaneous information |
18.2. |
| Title |
C[infinity] and approximation of integrable functions -- |
| Miscellaneous information |
18.3. |
| Title |
Tensor algebra and determinants -- |
| Miscellaneous information |
18.4. |
| Title |
Multidimensional substitution -- |
| Miscellaneous information |
19. |
| Title |
Manifolds and integral theorems -- |
| Miscellaneous information |
19.1. |
| Title |
Manifolds -- |
| Miscellaneous information |
19.2. |
| Title |
Tangent spaces and differentiable functions -- |
| Miscellaneous information |
19.3. |
| Title |
Differential forms, integrals over the unit cube -- |
| Miscellaneous information |
19.4. |
| Title |
k-forms and integrals over k-chains -- |
| Miscellaneous information |
19.5. |
| Title |
Integration on manifolds -- |
| Miscellaneous information |
g 19.6. |
| Title |
Stokes' theorem -- |
| Miscellaneous information |
20. |
| Title |
Hilbert spaces -- |
| Miscellaneous information |
20.1. |
| Title |
Orthonormal bases -- |
| Miscellaneous information |
20.2. |
| Title |
Fourier series -- |
| Miscellaneous information |
20.3. |
| Title |
The Riesz representation theorem -- |
| 505 00 - FORMATTED CONTENTS NOTE |
|---|
| Miscellaneous information |
pt. 3. |
| Title |
Applied analysis -- |
| Miscellaneous information |
21. |
| Title |
Physics background -- |
| Miscellaneous information |
21.1. |
| Title |
Harmonic oscillators -- |
| Miscellaneous information |
21.2. |
| Title |
Heat and diffusion -- |
| Miscellaneous information |
21.3. |
| Title |
Separation of variables, Fourier series, and ordinary differential equations -- |
| Miscellaneous information |
21.4. |
| Title |
Maxwell's equations -- |
| Miscellaneous information |
21.5. |
| Title |
The Navier Stokes equation for the conservation of mass -- |
| Miscellaneous information |
22. |
| Title |
Ordinary differential equations -- |
| Miscellaneous information |
22.1. |
| Title |
Banach space valued differential equations -- |
| Miscellaneous information |
22.2. |
| Title |
An existence and uniqueness theorem -- |
| Miscellaneous information |
22.3. |
| Title |
Linear differential equations -- |
| Miscellaneous information |
23. |
| Title |
The finite element method -- |
| Miscellaneous information |
23.1. |
| Title |
Ritz-Galerkin approximation -- |
| Miscellaneous information |
23.2. |
| Title |
Weakly differentiable functions -- |
| Miscellaneous information |
23.3. |
| Title |
Sobolev spaces -- |
| Miscellaneous information |
23.4. |
| Title |
Elliptic differential operators -- |
| Miscellaneous information |
23.5. |
| Title |
Finite elements -- |
| -- |
Conclusions and outlook -- |
| -- |
Appendices -- |
| Miscellaneous information |
A. |
| Title |
Logic -- |
| Miscellaneous information |
A.1. |
| Title |
Statements -- |
| Miscellaneous information |
A.2. |
| Title |
Negations -- |
| Miscellaneous information |
B. |
| Title |
Set theory -- |
| Miscellaneous information |
B.1. |
| Title |
The Zermelo-Fraenkel axioms -- |
| Miscellaneous information |
B.2. |
| Title |
Relations and functions -- |
| Miscellaneous information |
C. |
| Title |
Natural numbers, integers, and rational numbers -- |
| Miscellaneous information |
C.1. |
| Title |
The natural numbers -- |
| Miscellaneous information |
C.2. |
| Title |
The integers -- |
| Miscellaneous information |
C.3. |
| Title |
The rational numbers -- |
| -- |
Bibliography -- |
| -- |
Index. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematical analysis. |
| 856 41 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Materials specified |
Table of contents only |
| Uniform Resource Identifier |
<a href="http://www.loc.gov/catdir/toc/ecip0720/2007024690.html">http://www.loc.gov/catdir/toc/ecip0720/2007024690.html</a> |
| 856 42 - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Publisher description |
| Uniform Resource Identifier |
<a href="http://www.loc.gov/catdir/enhancements/fy0741/2007024690-d.html">http://www.loc.gov/catdir/enhancements/fy0741/2007024690-d.html</a> |
| 856 42 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Materials specified |
Contributor biographical information |
| Uniform Resource Identifier |
<a href="http://www.loc.gov/catdir/enhancements/fy0806/2007024690-b.html">http://www.loc.gov/catdir/enhancements/fy0806/2007024690-b.html</a> |
| 906 ## - LOCAL DATA ELEMENT F, LDF (RLIN) |
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| a |
7 |
| b |
cbc |
| c |
orignew |
| d |
1 |
| e |
ecip |
| f |
20 |
| g |
y-gencatlg |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Item type |
Books |
