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Principles of Mathematical Analysis by Walter Rudin (English) Hardcover Book
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Specificaties
- Objectstaat
- ISBN-13
- 9780070542358
- Book Title
- Principles of Mathematical Analysis
- ISBN
- 9780070542358
Over dit product
Product Identifiers
Publisher
Mcgraw-Hill Education
ISBN-10
007054235X
ISBN-13
9780070542358
eBay Product ID (ePID)
8038209331
Product Key Features
Number of Pages
352 Pages
Language
English
Publication Name
Principles of Mathematical Analysis
Subject
General, Mathematical Analysis
Publication Year
1976
Features
Revised
Type
Textbook
Subject Area
Mathematics
Format
Hardcover
Dimensions
Item Height
0.9 in
Item Weight
22.4 Oz
Item Length
9.2 in
Item Width
6.4 in
Additional Product Features
Edition Number
3
Intended Audience
College Audience
LCCN
75-017903
Dewey Edition
21
Dewey Decimal
517
Edition Description
Revised edition
Table Of Content
Chapter 1: The Real and Complex Number Systems Introduction Ordered Sets Fields The Real Field The Extended Real Number System The Complex Field Euclidean Spaces Appendix Exercises Chapter 2: Basic Topology Finite, Countable, and Uncountable Sets Metric Spaces Compact Sets Perfect Sets Connected Sets Exercises Chapter 3: Numerical Sequences and Series Convergent Sequences Subsequences Cauchy Sequences Upper and Lower Limits Some Special Sequences Series Series of Nonnegative Terms The Number e The Root and Ratio Tests Power Series Summation by Parts Absolute Convergence Addition and Multiplication of Series Rearrangements Exercises Chapter 4: Continuity Limits of Functions Continuous Functions Continuity and Compactness Continuity and Connectedness Discontinuities Monotonic Functions Infinite Limits and Limits at Infinity Exercises Chapter 5: Differentiation The Derivative of a Real Function Mean Value Theorems The Continuity of Derivatives L'Hospital's Rule Derivatives of Higher-Order Taylor's Theorem Differentiation of Vector-valued Functions Exercises Chapter 6: The Riemann-Stieltjes Integral Definition and Existence of the Integral Properties of the Integral Integration and Differentiation Integration of Vector-valued Functions Rectifiable Curves Exercises Chapter 7: Sequences and Series of Functions Discussion of Main Problem Uniform Convergence Uniform Convergence and Continuity Uniform Convergence and Integration Uniform Convergence and Differentiation Equicontinuous Families of Functions The Stone-Weierstrass Theorem Exercises Chapter 8: Some Special Functions Power Series The Exponential and Logarithmic Functions The Trigonometric Functions The Algebraic Completeness of the Complex Field Fourier Series The Gamma Function Exercises Chapter 9: Functions of Several Variables Linear Transformations Differentiation The Contraction Principle The Inverse Function Theorem The Implicit Function Theorem The Rank Theorem Determinants Derivatives of Higher Order Differentiation of Integrals Exercises Chapter 10: Integration of Differential Forms Integration Primitive Mappings Partitions of Unity Change of Variables Differential Forms Simplexes and Chains Stokes' Theorem Closed Forms and Exact Forms Vector Analysis Exercises Chapter 11: The Lebesgue Theory Set Functions Construction of the Lebesgue Measure Measure Spaces Measurable Functions Simple Functions Integration Comparison with the Riemann Integral Integration of Complex Functions Functions of Class L 2 Exercises Bibliography List of Special Symbols Index
Synopsis
The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.
LC Classification Number
QA303
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