Analysis I: Third Edition

Analysis I: Third Edition
ISBN-10
9811017891
ISBN-13
9789811017896
Series
Analysis I
Category
Mathematics
Pages
350
Language
English
Published
2016-08-29
Publisher
Springer
Author
Terence Tao

Description

This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

Get the book

Amazon.com
Amazon.com
Search the book
eBay.com
eBay.com
Search the book

Other editions

Similar books

  • Analysis
    Analysis
    By Terence Tao

    Suitable for undergraduates who have already been exposed to calculus, this title includes material that starts at the very beginning - the construction of number systems and set theory, then goes on to the basics of analysis, through to ...

  • Analysis I
    Analysis I
    By Herbert Amann, Joachim Escher

    "This textbook provides an outstanding introduction to analysis.

  • Functional Analysis I: Linear Functional Analysis
    Functional Analysis I: Linear Functional Analysis
    By Yu.I. Lyubich

    This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach.

  • PHARMACEUTICAL ANALYSIS-I
    PHARMACEUTICAL ANALYSIS-I

    ... analysis may be classified into four kinds (i) (ii) (iii) (iv) Proximate Analysis: It determines the amount of each element in a sample with no concern as to the actual compounds present. Partial Analysis: It deals with the ...

  • Circuit Analysis I: With Matlab Computing and Simulink/SimPowerSystems Modeling
    Circuit Analysis I: With Matlab Computing and Simulink/SimPowerSystems Modeling
    By Steven T. Karris

    This text is an introduction to the basic principles of electrical engineering and covers DC and AC circuit analysis and Transients.

  • Commutative Harmonic Analysis I: General Survey. Classical Aspects
    Commutative Harmonic Analysis I: General Survey. Classical Aspects
    By V.P. Khavin, N.K. Nikol'skij

    ... Analysis Volume 13 : R. V. Gamkrelidze ( Ed . ) Analysis I Integral Representations and Asymptotic Methods 1989. VII , 238 pp . ISBN 3-540-17008-1 Volume 14 : R. V. Gamkrelidze ( Ed . ) Analysis II Convex Analysis and Approximation ...

  • Mathematical Analysis I
    Mathematical Analysis I
    By Claudio Canuto, Anita Tabacco

    This new edition features additional material with the aim of matching the widest range of educational choices for a first course of Mathematics. The purpose of the volume is to provide a support for a first course in Mathematics.

  • Feminist Critical Policy Analysis I
    Feminist Critical Policy Analysis I
    By Catherine Marshall

    eliminate sexual harassment actually reinforce the hierarchical, sex-segregated structure and power differentials ... Implementation of sexual harassment policies is problematic since no federal, state or local government agency is ...

  • Mathematical Analysis I
    Mathematical Analysis I
    By Vladimir A. Zorich

    This work by Zorich on Mathematical Analysis constitutes a thorough first course in real analysis, leading from the most elementary facts about real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, ...

  • Problems and Theorems in Analysis I: Series. Integral Calculus. Theory of Functions
    Problems and Theorems in Analysis I: Series. Integral Calculus. Theory of Functions
    By George Pólya, Gábor Szegő

    Moreover tyu + fxv + t , = 0 . This leads to a contradiction : Put F = tu + tv + tart = yz + zx + xy . Then ƏF 22F F fx + - 22 . ay ду Second proof : Take the derivatives with respect to x , y , z and set % = -y in the three ...