000			06013nam a2200385 i 4500
008			081031r20092006riua 001 0 eng
010			_a2008047395
020			_a9780821847916 _qalk. paper
020			_a0821847910 _qalk. paper
035			_a.b66106916
040			_aDLC _beng _cDLC _dYDXCP _dC#P _dUtOrBLW _dBAUN _erda
049			_aBAUN_MERKEZ
050	0	4	_aQA303.2 _b.F58 2009
082	0	0	_222
100	1		_aFitzpatrick, Patrick, _d1946-
245	1	0	_aAdvanced calculus / _cPatrick M. Fitzpatrick
250			_a2nd ed
264		1	_aProvidence, R.I. : _bAmerican Mathematical Society, _c[2009?]
300			_axviii, 590 pages : _billustrations ; _c24 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	1		_aPure and applied undergraduate texts ; _v5
490	1		_aThe Sally series
500			_aOriginally published: 2nd edition Belmont, CA : Thomson Brooks/Cole, c2006
500			_aIncludes index
505	0	0	_tTable Of Contents: _tPreface _tPreliminaries _t1 TOOLS FOR ANALYSIS _t1.1 The Completeness Axiom and Some of Its Consequences _t1.2 The Distribution of the Integers and the Rational Numbers _t1.3 Inequalities and Identities _t2 CONVERGENT SEQUENCES _t2.1 The Convergence of Sequences _t2.2 Sequences and Sets _t2.3 The Monotone Convergence Theorem _t2.4 The Sequential Compactness Theorem _t2.5 Covering Properties of Sets* _t3 CONTINUOUS FUNCTIONS _t3.1 Continuity _t3.2 The Extreme Value Theorem _t3.3 The Intermediate Value Theorem _t3.4 Uniform Continuity _t3.5 The element of-δ Criterion for Continuity _t3.6 Images and Inverses; Monotone Functions _t3.7 Limits _t4 DIFFERENTIATION _t4.1 The Algebra of Derivatives _t4.2 Differentiating Inverses and Compositions _t4.3 The Mean Value Theorem and Its Geometric Consequences _t4.4 The Cauchy Mean Value Theorem and Its Analytic Consequences _t4.5 The Notation of Leibnitz _t5 ELEMENTARY FUNCTIONS AS SOLUTIONS OF DIFFERENTIAL EQUATIONS _t5.1 Solutions of Differential Equations _t5.2 The Natural Logarithm and Exponential Functions _t5.3 The Trigonometric Functions _t5.4 The Inverse Trigonometric Functions _t6 INTEGRATION: TWO FUNDAMENTAL THEOREMS _t6.1 Darboux Sums; Upper and Lower Integrals _t6.2 The Archimedes—Riemann Theorem _t6.3 Additivity, Monotonicity, and Linearity _t6.4 Continuity and Integrability _t6.5 The First Fundamental Theorem: Integrating Derivatives _t6.6 The Second Fundamental Theorem: Differentiating Integrals _t7 INTEGRATION: FURTHER TOPICS _t7.1 Solutions of Differential Equations _t7.2 Integration by Parts and by Substitution _t7.3 The Convergence of Darboux and Riemann Sums _t7.4 The Approximation of Integrals _t8 APPROXIMATION BY TAYLOR POLYNOMIALS _t8.1 Taylor Polynomials _t8.2 The Lagrange Remainder Theorem _t8.3 The Convergence of Taylor Polynomials _t8.4 A Power Series for the Logarithm _t8.5 The Cauchy Integral Remainder Theorem _t8.6 A Nonanalytic, Infinitely Differentiable Function _t8.7 The Weierstrass Approximation Theorem _t9 SEQUENCES AND SERIES OF FUNCTIONS _t9.1 Sequences and Series of Numbers _t9.2 Pointwise Convergence of Sequences of Functions _t9.3 Uniform Convergence of Sequences of Functions _t9.4 The Uniform Limit of Functions _t9.5 Power Series _t9.6 A Continuous Nowhere Differentiable Function _t10 THE EUCLIDEAN SPACE Rn _t10.1 The Linear Structure of Rn and the Scalar Product _t10.2 Convergence of Sequences in Rn _t10.3 Open Sets and Closed Sets in Rn _t11 CONTINUITY, COMPACTNESS, AND CONNECTEDNESS _t11.1 Continuous Functions and Mappings _t11.2 Sequential Compactness, Extreme Values, and Uniform Continuity _t11.3 Pathwise Connectedness and the Intermediate Value Theorem* _t11.4 Connectedness and the Intermediate Value Property* _t12 METRIC SPACES _t12.1 Open Sets, Closed Sets, and Sequential Convergence _t12.2 Completeness and the Contraction Mapping Principle _t12.3 The Existence Theorem for Nonlinear Differential Equations _t12.4 Continuous Mappings between Metric Spaces _t12.5 Sequential Compactness and Connectedness _t13 DIFFERENTIATING FUNCTIONS OF SEVERAL VARIABLES _t13.1 Limits _t13.2 Partial Derivatives _t13.3 The Mean Value Theorem and Directional Derivatives _t14 LOCAL APPROXIMATION OF REAL-VALUED FUNCTIONS _t14.1 First-Order Approximation, Tangent Planes, and Affine Functions _t14.2 Quadratic Functions, Hessian Matrices, and Second Derivatives* _t14.3 Second-Order Approximation and the Second-Derivative Test* _t15 APPROXIMATING NONLINEAR MAPPINGS BY LINEAR MAPPINGS _t15.1 Linear Mappings and Matrices _t15.2 The Derivative Matrix and the Differential _t15.3 The Chain Rule _t16 IMAGES AND INVERSES: THE INVERSE FUNCTION THEOREM _t16.1 Functions of a Single Variable and Maps in the Plane _t16.2 Stability of Nonlinear Mappings _t16.3 A Minimization Principle and the General Inverse Function Theorem _t17 THE IMPLICIT FUNCTION THEOREM AND ITS APPLICATIONS _t17.1 A Scalar Equation in Two Unknowns: Dini's Theorem _t17.2 The General Implicit Function Theorem _t17.3 Equations of Surfaces and Paths in R³ _t17.4 Constrained Extrema Problems and Lagrange Multipliers _t18 INTEGRATING FUNCTIONS OF SEVERAL VARIABLES _t18.1 Integration of Functions on Generalized Rectangles _t18.2 Continuity and Integrability _t18.3 Integration of Functions on Jordan Domains _t19 ITERATED INTEGRATION AND CHANGES OF VARIABLES _t19.1 Fubini's Theorem _t19.2 The Change of Variables Theorem: Statements and Examples _t19.3 Proof of the Change of Variables Theorem _t20 LINE AND SURFACE INTEGRALS _t20.1 Arclength and Line Integrals _t20.2 Surface Area and Surface Integrals _t20.3 The Integral Formulas of Green and Stokes _tA CONSEQUENCES OF THE FIELD AND POSITIVITY AXIOMS _tA.1 The Field Axioms and Their Consequences _tA.2 The Positivity Axioms and Their Consequences _tB LINEAR ALGEBRA _tIndex
650		0	_aCalculus _vTextbooks
710	2		_9111032 _aAmerican Mathematical Society.
830		0	_920582 _aPure and applied undergraduate texts ; _v5
830		0	_920581 _aSally series (Providence, R.I.)
900			_a31560
900			_bsatın
942			_2lcc _cKT
999			_c28433 _d28433