MARC ayrıntıları
| 000 -LEADER |
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| fixed length control field |
06013nam a2200385 i 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
081031r20092006riua 001 0 eng |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER |
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| LC control number |
2008047395 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780821847916 |
| Qualifying information |
alk. paper |
|
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| International Standard Book Number |
0821847910 |
| Qualifying information |
alk. paper |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
.b66106916 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
DLC |
| Language of cataloging |
eng |
| Transcribing agency |
DLC |
| Modifying agency |
YDXCP |
| -- |
C#P |
| -- |
UtOrBLW |
| -- |
BAUN |
| Description conventions |
rda |
| 049 ## - LOCAL HOLDINGS (OCLC) |
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| Holding library |
BAUN_MERKEZ |
| 050 04 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA303.2 |
| Item number |
.F58 2009 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Edition number |
22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Fitzpatrick, Patrick, |
| Dates associated with a name |
1946- |
| 245 10 - TITLE STATEMENT |
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| Title |
Advanced calculus / |
| Statement of responsibility, etc |
Patrick M. Fitzpatrick |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
2nd ed |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Place of production, publication, distribution, manufacture |
Providence, R.I. : |
| Name of producer, publisher, distributor, manufacturer |
American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice |
[2009?] |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xviii, 590 pages : |
| Other physical details |
illustrations ; |
| Dimensions |
24 cm |
| 336 ## - CONTENT TYPE |
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| Content Type Term |
text |
| Content Type Code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media Type Term |
unmediated |
| Media Type Code |
unmediated |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier Type Term |
volume |
| Carrier Type Code |
volume |
| Source |
rdacarrier |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Pure and applied undergraduate texts ; |
| Volume number/sequential designation |
5 |
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| Series statement |
The Sally series |
| 500 ## - GENERAL NOTE |
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| General note |
Originally published: 2nd edition Belmont, CA : Thomson Brooks/Cole, c2006 |
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| General note |
Includes index |
| 505 00 - FORMATTED CONTENTS NOTE |
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| Title |
Table Of Contents: |
| -- |
Preface |
| -- |
Preliminaries |
| -- |
1 TOOLS FOR ANALYSIS |
| -- |
1.1 The Completeness Axiom and Some of Its Consequences |
| -- |
1.2 The Distribution of the Integers and the Rational Numbers |
| -- |
1.3 Inequalities and Identities |
| -- |
2 CONVERGENT SEQUENCES |
| -- |
2.1 The Convergence of Sequences |
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2.2 Sequences and Sets |
| -- |
2.3 The Monotone Convergence Theorem |
| -- |
2.4 The Sequential Compactness Theorem |
| -- |
2.5 Covering Properties of Sets* |
| -- |
3 CONTINUOUS FUNCTIONS |
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3.1 Continuity |
| -- |
3.2 The Extreme Value Theorem |
| -- |
3.3 The Intermediate Value Theorem |
| -- |
3.4 Uniform Continuity |
| -- |
3.5 The element of-δ Criterion for Continuity |
| -- |
3.6 Images and Inverses; Monotone Functions |
| -- |
3.7 Limits |
| -- |
4 DIFFERENTIATION |
| -- |
4.1 The Algebra of Derivatives |
| -- |
4.2 Differentiating Inverses and Compositions |
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4.3 The Mean Value Theorem and Its Geometric Consequences |
| -- |
4.4 The Cauchy Mean Value Theorem and Its Analytic Consequences |
| -- |
4.5 The Notation of Leibnitz |
| -- |
5 ELEMENTARY FUNCTIONS AS SOLUTIONS OF DIFFERENTIAL EQUATIONS |
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5.1 Solutions of Differential Equations |
| -- |
5.2 The Natural Logarithm and Exponential Functions |
| -- |
5.3 The Trigonometric Functions |
| -- |
5.4 The Inverse Trigonometric Functions |
| -- |
6 INTEGRATION: TWO FUNDAMENTAL THEOREMS |
| -- |
6.1 Darboux Sums; Upper and Lower Integrals |
| -- |
6.2 The Archimedes—Riemann Theorem |
| -- |
6.3 Additivity, Monotonicity, and Linearity |
| -- |
6.4 Continuity and Integrability |
| -- |
6.5 The First Fundamental Theorem: Integrating Derivatives |
| -- |
6.6 The Second Fundamental Theorem: Differentiating Integrals |
| -- |
7 INTEGRATION: FURTHER TOPICS |
| -- |
7.1 Solutions of Differential Equations |
| -- |
7.2 Integration by Parts and by Substitution |
| -- |
7.3 The Convergence of Darboux and Riemann Sums |
| -- |
7.4 The Approximation of Integrals |
| -- |
8 APPROXIMATION BY TAYLOR POLYNOMIALS |
| -- |
8.1 Taylor Polynomials |
| -- |
8.2 The Lagrange Remainder Theorem |
| -- |
8.3 The Convergence of Taylor Polynomials |
| -- |
8.4 A Power Series for the Logarithm |
| -- |
8.5 The Cauchy Integral Remainder Theorem |
| -- |
8.6 A Nonanalytic, Infinitely Differentiable Function |
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8.7 The Weierstrass Approximation Theorem |
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9 SEQUENCES AND SERIES OF FUNCTIONS |
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9.1 Sequences and Series of Numbers |
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9.2 Pointwise Convergence of Sequences of Functions |
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9.3 Uniform Convergence of Sequences of Functions |
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9.4 The Uniform Limit of Functions |
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9.5 Power Series |
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9.6 A Continuous Nowhere Differentiable Function |
| -- |
10 THE EUCLIDEAN SPACE Rn |
| -- |
10.1 The Linear Structure of Rn and the Scalar Product |
| -- |
10.2 Convergence of Sequences in Rn |
| -- |
10.3 Open Sets and Closed Sets in Rn |
| -- |
11 CONTINUITY, COMPACTNESS, AND CONNECTEDNESS |
| -- |
11.1 Continuous Functions and Mappings |
| -- |
11.2 Sequential Compactness, Extreme Values, and Uniform Continuity |
| -- |
11.3 Pathwise Connectedness and the Intermediate Value Theorem* |
| -- |
11.4 Connectedness and the Intermediate Value Property* |
| -- |
12 METRIC SPACES |
| -- |
12.1 Open Sets, Closed Sets, and Sequential Convergence |
| -- |
12.2 Completeness and the Contraction Mapping Principle |
| -- |
12.3 The Existence Theorem for Nonlinear Differential Equations |
| -- |
12.4 Continuous Mappings between Metric Spaces |
| -- |
12.5 Sequential Compactness and Connectedness |
| -- |
13 DIFFERENTIATING FUNCTIONS OF SEVERAL VARIABLES |
| -- |
13.1 Limits |
| -- |
13.2 Partial Derivatives |
| -- |
13.3 The Mean Value Theorem and Directional Derivatives |
| -- |
14 LOCAL APPROXIMATION OF REAL-VALUED FUNCTIONS |
| -- |
14.1 First-Order Approximation, Tangent Planes, and Affine Functions |
| -- |
14.2 Quadratic Functions, Hessian Matrices, and Second Derivatives* |
| -- |
14.3 Second-Order Approximation and the Second-Derivative Test* |
| -- |
15 APPROXIMATING NONLINEAR MAPPINGS BY LINEAR MAPPINGS |
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15.1 Linear Mappings and Matrices |
| -- |
15.2 The Derivative Matrix and the Differential |
| -- |
15.3 The Chain Rule |
| -- |
16 IMAGES AND INVERSES: THE INVERSE FUNCTION THEOREM |
| -- |
16.1 Functions of a Single Variable and Maps in the Plane |
| -- |
16.2 Stability of Nonlinear Mappings |
| -- |
16.3 A Minimization Principle and the General Inverse Function Theorem |
| -- |
17 THE IMPLICIT FUNCTION THEOREM AND ITS APPLICATIONS |
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17.1 A Scalar Equation in Two Unknowns: Dini's Theorem |
| -- |
17.2 The General Implicit Function Theorem |
| -- |
17.3 Equations of Surfaces and Paths in R³ |
| -- |
17.4 Constrained Extrema Problems and Lagrange Multipliers |
| -- |
18 INTEGRATING FUNCTIONS OF SEVERAL VARIABLES |
| -- |
18.1 Integration of Functions on Generalized Rectangles |
| -- |
18.2 Continuity and Integrability |
| -- |
18.3 Integration of Functions on Jordan Domains |
| -- |
19 ITERATED INTEGRATION AND CHANGES OF VARIABLES |
| -- |
19.1 Fubini's Theorem |
| -- |
19.2 The Change of Variables Theorem: Statements and Examples |
| -- |
19.3 Proof of the Change of Variables Theorem |
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20 LINE AND SURFACE INTEGRALS |
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20.1 Arclength and Line Integrals |
| -- |
20.2 Surface Area and Surface Integrals |
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20.3 The Integral Formulas of Green and Stokes |
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A CONSEQUENCES OF THE FIELD AND POSITIVITY AXIOMS |
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A.1 The Field Axioms and Their Consequences |
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A.2 The Positivity Axioms and Their Consequences |
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B LINEAR ALGEBRA |
| -- |
Index |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Calculus |
| Form subdivision |
Textbooks |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| 9 (RLIN) |
111032 |
| Corporate name or jurisdiction name as entry element |
American Mathematical Society. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| 9 (RLIN) |
20582 |
| Uniform title |
Pure and applied undergraduate texts ; |
| Volume number/sequential designation |
5 |
|
|---|
| 9 (RLIN) |
20581 |
| Uniform title |
Sally series (Providence, R.I.) |
| 900 ## - EQUIVALENCE OR CROSS-REFERENCE-PERSONAL NAME [LOCAL, CANADA] |
|---|
| Personal Name |
31560 |
|
|---|
| Numeration |
satın |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
Library of Congress Classification |
| Koha item type |
Kitap |
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