Principles of Mathematical Analysis

Principles of Mathematical Analysis (English, Paperback, Rudin Walter)

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Principles of Mathematical Analysis  (English, Paperback, Rudin Walter)

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    Highlights
    • Language: English
    • Binding: Paperback
    • Publisher: Mcgraw Hill
    • Genre: Mathematics
    • ISBN: 9781259064784, 1259064786
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  • Description

    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.

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    Specifications
    Book Details
    Imprint
    • India Higher Education
    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
    University Books Details
    Specialization
    • B.Sc(Mathematics)
    Dimensions
    Width
    • 33 mm
    Height
    • 579 mm
    Length
    • 388 mm
    Weight
    • 158 gr
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    Ratings & Reviews
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    201 Ratings &
    20 Reviews
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    5

    Perfect product!

    This is a very good book for master level
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    Anshuman Pradhan

    Certified Buyer, Kalahandi District

    6 months ago

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    5

    Best book for Analysis(Baby rudin)

    Mathematicians around the world commonly call this book as "babyrudin"..If you are new to analysis dont read this, may be read one of this "malik s arora or Arumugam isaac or n.p.bali" and then try this babyrudin book.
    before buying this, i bought the same book from another online website few months back due to the price(may be 20 to 30 ruppes less than flipkart), the quality of the book is not that much good, the two pages got printed in a single page made it impossible to read..So decided n...
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    Christopher

    Certified Buyer, Ramanathapuram

    Apr, 2016

    6
    5
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    5

    Must buy!

    Best book if you are ready to invest some time in it. If you are from non mathematics background then refer to Harvey Mudd college's "Analysis Yawp!" (video quality is bad but lectures are awesome). Helps you gain confidence to read and understand the book.
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    Madhusudan Sinha

    Certified Buyer, Chennai

    9 months ago

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    5

    Great product

    I m too beginner... To say anything about this great book!! But i would say... Read this book when u think that u r master in real analysis... And this will prove u wrong.!!
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    uttam kumar gupta

    Certified Buyer, Ranchi

    10 months ago

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    5

    Mind-blowing purchase

    must buy book for ug, pg and research leve.l got it for less price, flip cart seller, true comretail
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    Flipkart Customer

    Certified Buyer, Bengaluru

    May, 2018

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    5

    Terrific

    Very humble and responding.
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    Anup Yakthungba

    Certified Buyer, Gangtok

    Nov, 2017

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    3

    Decent product

    Some of the things are explained in a well manner but read some basic books before it ..topological language might be difficult without understanding basic concepts
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    Flipkart Customer

    Certified Buyer, Hiranagar

    Oct, 2017

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    5

    Not for a single reading

    If you've ever felt there were gaps in the reasoning behind calculus, if you felt something was fishy about the proofs in school, finish this book, I don't use the word read because one doesn't simply read this book. You have to pick a fight with it. It is generally not advisable as a first book for beginners, but if you are brave enough you can tackle it right away, if you want to be a mathematician even after finishing this book you are a mathematician, if you want to be a mathematician ev...
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    Flipkart Customer

    Certified Buyer, Hyderabad

    Sep, 2017

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    5

    Great product

    Nice product
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    Vivek Prakash

    Certified Buyer, Medinipur

    May, 2017

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    5

    Good book

    It's good with affordable price and I am so satisfied by product. delivered on time.
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    Kushal Mondal

    Certified Buyer, Kolkata

    May, 2017

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    All 20 reviews
    Questions and Answers
    Q:what is it's level?
    A:Undergraduate
    Kirtan vora
    Certified Buyer
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    Q:can this book be used for iit preparetion
    A:This book is a graduate level book for real analysis. If you are referring to JEE Advanced, then it is not the book you should look for.
    Anonymous
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