000			04173nam a2200337 i 4500
001			430
005			20260205155216.0
008			921030s1993 nyua b 001 0 eng
010			_a92041432
020			_a0716721058
035			_a.b42722366
040			_aDLC _cDLC _dOSU
041	0		_aeng
049			_aBAUN_MERKEZ
050	0	4	_aQA300 _b.M2868 1993
082	0	0	_220
100	1		_aMarsden, Jerrold E _990090 _eaut
245	1	0	_aElementary classical analysis / _cJerrold E. Marsden, Michael J. Hoffman
250			_a2nd ed
264		1	_aNew York : _bW.H. Freeman, _c[1993]
264		4	_c©1993
300			_axiv, 738 pages : _billustrations ; _c25 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
504			_aIncludes bibliographical references and index
505	0	0	_tContents _tPreface _tPreface to the First Edition _tIntroduction: Sets and Functions _t1 The Real Line and Euclidean Space _t1.1 Ordered Fields and the Number System _t1.2 Completeness and the Real Number System _t1.3 Least Upper Bounds _t1.4 Cauchy Sequences _t1.5 Cluster Points; lim inf and lim sup _t1.6 Euclidean Space _t1.7 Norms, Inner Products, and Metrics _t1.8 The Complex Numbers _t2 The Topology of Euclidean Space _t2.1 Open Sets _t2.2 Interior of a Set _t2.3 Closed Sets _t2.4 Accumulation Points _t2.5 Closure of a Set _t2.6 Boundary of a Set _t2.7 Sequences _t2.8 Completeness _t2.9 Series of Real Numbers and Vectors _t3 Compact and Connected Sets _t3.1 Compactness _t3.2 The Heine-Borel Theorem _t3.3 Nested Set Property _t3.4 Path-Connected Sets _t3.5 Connected Sets _t4 Continuous Mappings _t4.1 Continuity _t4.2 Images of Compact and Connected Sets _t4.3 Operations on Continuous Mappings _t4.4 The Boundedness of Continuous Functions on Compact Sets _t4.5 The Intermediate Value Theorem _t4.6 Uniform Continuity _t4.7 Differentiation of Functions of One Variable _t4.8 Integration of Functions of One Variable _t5 Uniform Convergence _t5.1 Pointwise and Uniform Convergence _t5.2 The Weierstrass M Test _t5.3 Integration and Differentiation of Series _t5.4 The Elementary Functions _t5.5 The Space of Continuous Functions _t5.6 The Arzela-Ascoli Theorem _t5.7 The Contraction Mapping Principle and Its Applications _t5.8 The Stone-Weierstrass Theorem _t5.9 The Dirichlet and Abel Tests _t5.10 Power Series and Cesaro and Abel Summability _t6 Differentiable Mappings _t6.1 Definition of the Derivative _t6.2 Matrix Representation _t6.3 Continuity of Differentiable Mappings; Differentiable Paths _t6.4 Conditions for Differentiability _t6.5 The Chain Rule _t6.6 Product Rule and Gradients _t6.7 The Mean Value Theorem _t6.8 Taylor's Theorem and Higher Derivatives _t6.9 Maxima and Minima _t7 The Inverse and Implicit Function Theorems and Related Topics _t7.1 Inverse Function Theorem _t7.2 Implicit Function Theorem _t7.3 The Domain-Straightening Theorem _t7.4 Further Consequences of the Implicit Function Theorem _t7.5 An Existence Theorem for Ordinary Differential Equations _t7.6 The Morse Lemma _t7.7 Constrained Extrema and Lagrange Multipliers _t8 Integration _t8.1 Integrable Functions _t8.2 Volume and Sets of Measure Zero _t8.3 Lebesgue's Theorem _t8.4 Properties of the Integral _t8.5 Improper Integrals _t8.6 Some Convergence Theorems _t8.7 Introduction to Distributions _t9 Fubini's Theorem and the Change of Variables Formula _t9.2 Fubini's Theorem _t9.3 Change of Variables Theorem _t9.4 Polar Coordinates _t9.5 Spherical and Cylindrical Coordinates _t9.6 A Note on the Lebesgue Integral _t9.7 Interchange of Limiting Operations _t10 Fourier Analysis _t10.1 Inner Product Spaces _t10.2 Orthogonal Families of Functions _t10.3 Completeness and Convergence Theorems _t10.4 Functions of Bounded Variation and Fejer Theory (Optional) _t10.5 Computation of Fourier Series _t10.6 Further Convergence Theorems _t10.7 Applications _t10.8 Fourier Integrals _t10.9 Quantum Mechanical Formalism _tAppendix A: Miscellaneous Exercises _tAppendix B: References and Suggestions for Further Study _tAppendix C: Answers and Suggestions for Selected Odd-Numbered Exercises _tIndex
650		0	_aMathematical analysis _91914
700	1		_aHoffman, Michael J _9122863 _eaut
942			_2lcc _cKT
999			_c16524 _d16524