Principles of mathematical analysis / Walter Rudin.
Series International series in pure and applied mathematicsEditor: New York : McGraw-Hill, c1976Edición: 3rd edDescripción: x, 342 p. ; 24 cmISBN: 007054235XTema(s): Mathematical analysisOtra clasificación: 26-01 Recursos en línea: Table of contentsPreface ix Chapter [1] The Real and Complex Number Systems [1] Introduction [1] Ordered Sets [3] Fields [5] The Real Field [8] The Extended Real Number System [11] The Complex Field [12] Euclidean Spaces [16] Appendix [17] Exercises [21] Chapter [2] Basic Topology [24] Finite, Countable, and Uncountable Sets [24] Metric Spaces [30] Compact Sets [36] Perfect Sets [41] Connected Sets [42] Exercises [43] Chapter [3] Numerical Sequences and Series [47] Convergent Sequences [47] Subsequences [51] Cauchy Sequences [52] Upper and Lower Limits [55] Some Special Sequences [57] Series [58] Series of Nonnegative Terms [61] The Number e [63] The Root and Ratio Tests [65] Power Series [69] Summation by Parts [70] Absolute Convergence [71] Addition and Multiplication of Series [72] Rearrangements [75] Exercises [78] Chapter 4 Continuity [83] Limits of Functions [83] Continuous Functions [85] Continuity and Compactness [89] Continuity and Connectedness [93] Discontinuities [94] Monotonic Functions [95] Infinite Limits and Limits at Infinity [97] Exercises [98] Chapter 5 Differentiation [103] The Derivative of a Real Function [103] Mean Value Theorems [107] The Continuity of Derivatives [108] L’Hospital’s Rule [109] Derivatives of Higher Order [110] Taylor’s Theorem [110] Differentiation of Vector-valued Functions [111] Exercises [114] Chapter 6 The Riemann-Stieltjes Integral [120] Definition and Existence of the Integral [120] Properties of the Integral [128] Integration and Differentiation [133] Integration of Vector-valued Functions [135] Rectifiable Curves [136] Exercises [138] Chapter 7 Sequences and Series of Functions. [143] Discussion of Main Problem [143] Uniform Convergence [147] Uniform Convergence and Continuity [149] Uniform Convergence and Integration [151] Uniform Convergence and Differentiation [152] Equicontinuous Families of Functions [154] The Stone-Weierstrass Theorem [159] Exercises [165] Chapter 8 Some Special Functions [172] Power Series [172] The Exponential and Logarithmic Functions [178] The Trigonometric Functions [182] The Algebraic Completeness of the Complex Field [184] Fourier Series [185] The Gamma Function [192] Exercises [196] Chapter [9] Functions of Several Variables [204] Linear Transformations [204] Differentiation [211] The Contraction Principle [220] The Inverse Function Theorem [221] The Implicit Function Theorem [223] The Rank Theorem [228] Determinants [231] Derivatives of Higher Order [235] Differentiation of Integrals [236] Exercises [239] Chapter 10 Integration of Differential Forms [245] Integration [245] Primitive Mappings [248] Partitions of Unity [251] Change of Variables [252] Differential Forms [253] Simplexes and Chains [266] Stokes’ Theorem [273] Closed Forms and Exact Forms [275] Vector Analysis [280] Exercises [288] Chapter [11] The Lebesgue Theory [300] Set Functions [300] Construction of the Lebesgue Measure [302] Measure Spaces [310] Measurable Functions [310] Simple Functions [313] Integration [314] Comparison with the Riemann Integral [322] Integration of Complex Functions [325] Functions of Class L2 [325] Exercises [332] Bibliography [335] List of Special Symbols [337] Index [339]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 26 R916 (Browse shelf) | Checked out | 2024-05-20 | A-7084 |
Bibliografía: p. [335]-336.
Preface ix --
Chapter [1] --
The Real and Complex Number Systems [1] --
Introduction [1] --
Ordered Sets [3] --
Fields [5] --
The Real Field [8] --
The Extended Real Number System [11] --
The Complex Field [12] --
Euclidean Spaces [16] --
Appendix [17] --
Exercises [21] --
Chapter [2] --
Basic Topology [24] --
Finite, Countable, and Uncountable Sets [24] --
Metric Spaces [30] --
Compact Sets [36] --
Perfect Sets [41] --
Connected Sets [42] --
Exercises [43] --
Chapter [3] --
Numerical Sequences and Series [47] --
Convergent Sequences [47] --
Subsequences [51] --
Cauchy Sequences [52] --
Upper and Lower Limits [55] --
Some Special Sequences [57] --
Series [58] --
Series of Nonnegative Terms [61] --
The Number e [63] --
The Root and Ratio Tests [65] --
Power Series [69] --
Summation by Parts [70] --
Absolute Convergence [71] --
Addition and Multiplication of Series [72] --
Rearrangements [75] --
Exercises [78] --
Chapter 4 Continuity [83] --
Limits of Functions [83] --
Continuous Functions [85] --
Continuity and Compactness [89] --
Continuity and Connectedness [93] --
Discontinuities [94] --
Monotonic Functions [95] --
Infinite Limits and Limits at Infinity [97] --
Exercises [98] --
Chapter 5 Differentiation [103] --
The Derivative of a Real Function [103] --
Mean Value Theorems [107] --
The Continuity of Derivatives [108] --
L’Hospital’s Rule [109] --
Derivatives of Higher Order [110] --
Taylor’s Theorem [110] --
Differentiation of Vector-valued Functions [111] --
Exercises [114] --
Chapter 6 The Riemann-Stieltjes Integral [120] --
Definition and Existence of the Integral [120] --
Properties of the Integral [128] --
Integration and Differentiation [133] --
Integration of Vector-valued Functions [135] --
Rectifiable Curves [136] --
Exercises [138] --
Chapter 7 Sequences and Series of Functions. [143] --
Discussion of Main Problem [143] --
Uniform Convergence [147] --
Uniform Convergence and Continuity [149] --
Uniform Convergence and Integration [151] --
Uniform Convergence and Differentiation [152] --
Equicontinuous Families of Functions [154] --
The Stone-Weierstrass Theorem [159] --
Exercises [165] --
Chapter 8 Some Special Functions [172] --
Power Series [172] --
The Exponential and Logarithmic Functions [178] --
The Trigonometric Functions [182] --
The Algebraic Completeness of the Complex Field [184] --
Fourier Series [185] --
The Gamma Function [192] --
Exercises [196] --
Chapter [9] --
Functions of Several Variables [204] --
Linear Transformations [204] --
Differentiation [211] --
The Contraction Principle [220] --
The Inverse Function Theorem [221] --
The Implicit Function Theorem [223] --
The Rank Theorem [228] --
Determinants [231] --
Derivatives of Higher Order [235] --
Differentiation of Integrals [236] --
Exercises [239] --
Chapter 10 Integration of Differential Forms [245] --
Integration [245] --
Primitive Mappings [248] --
Partitions of Unity [251] --
Change of Variables [252] --
Differential Forms [253] --
Simplexes and Chains [266] --
Stokes’ Theorem [273] --
Closed Forms and Exact Forms [275] --
Vector Analysis [280] --
Exercises [288] --
Chapter [11] --
The Lebesgue Theory [300] --
Set Functions [300] --
Construction of the Lebesgue Measure [302] --
Measure Spaces [310] --
Measurable Functions [310] --
Simple Functions [313] --
Integration [314] --
Comparison with the Riemann Integral [322] --
Integration of Complex Functions [325] --
Functions of Class L2 [325] --
Exercises [332] --
Bibliography [335] --
List of Special Symbols [337] --
Index [339] --
MR, 52 #5893
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