Part of the Student Series in Advanced Mathematics, this book provides a foundation in mathematical analysis. It begins with a discussion of the real ...Show synopsisPart of the Student Series in Advanced Mathematics, this book provides a foundation in mathematical analysis. It begins with a discussion of the real number system as a complete ordered field. It also provides the topological background needed for the development of convergence, continuity, differentiation and integration.Hide synopsis
Description:New. The third edition of this well known text continues to...New. 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. TABLE OF CONTENTS 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 L2 Exercises Bibliography List of Special Symbols Index Printed Pages: 352. 15 x 23 cm.
Description:Fair. 3e Item is intact, but may show shelf wear. Pages may...Fair. 3e Item is intact, but may show shelf wear. Pages may include notes and highlighting. May or may not include supplemental or companion material. Access codes may or may not work. Connecting readers since 1972. Customer service is our top priority.
this book is thorough, and covers everything. it is terse, but because Rudin is trying to bring out the most salient points, not confuse you with trivial steps. This way he makes it clear what is interesting. At each point in his proofs, you should follow his logic and you'll see that he does make the right blend of instruction and hand-holding. Definitely showing that math is a do, not a see activity. He is also comprehensive and doesn't leave much out.
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