The Way of Analysis

כריכה קדמית
Jones & Bartlett Learning, 2000 - 739 עמודים
The Way of Analysis gives a thorough account of real analysis in one or several variables, from the construction of the real number system to an introduction of the Lebesgue integral. The text provides proofs of all main results, as well as motivations, examples, applications, exercises, and formal chapter summaries. Additionally, there are three chapters on application of analysis, ordinary differential equations, Fourier series, and curves and surfaces to show how the techniques of analysis are used in concrete settings.
 

עמודים נבחרים

תוכן

Preliminaries
1
Topology of the Real Line
3
Differential Calculus
5
Transcendental Functions
8
Implicit Functions Curves and Surfaces
13
Concepts of Continuity
14
Construction of the Real Number System
25
Exercises
34
Euclidean Space and Metric Spaces
355
Continuous Functions on Compact Domains
386
30
412
Differential Calculus in Euclidean Space
445
Ordinary Differential Equations
459
Fourier Series
522
The Lebesgue Integral
624
Multiple Integrals
698

Integral Calculus
201
Exercises
217
Sequences and Series of Functions
241
Approximating Derivatives
305
610
727
473
732
623
734
זכויות יוצרים

מהדורות אחרות - הצג הכל

The Way of Analysis
<span dir=ltr>Robert S. Strichartz</span>‏
הצגת קטע - 1995

מונחים וביטויים נפוצים

1/m there exists 1/n implies absolutely convergent approximation assume axiom of Archimedes Cauchy criterion Cauchy sequence Cauchy sums closed set compact set complex numbers construction contains continuous function Dedekind cut definition denote derivative difference quotient differentiable at xo discontinuities domain endpoints equivalence class error 1/n exercise f(xo fact finite number fn(x formula function f ƒ and g ƒ is continuous g(xo given any error implies f(x intuitive lemma Let f limit limit-point limsup mathematics mean value theorem metric space monotone increasing natural number neighborhood of xo obtain open interval open set Osc(f partition point xo polynomial positive power series proof properties prove rational numbers real number system Riemann integrable satisfies sequence of rationals sequence x1 shown in Figure statement subintervals subset sup and inf Taylor's theorem triangle inequality uniform convergence upper bound x-xo y₁ zero

הפניות לספר זה

מידע על המחבר (2000)

Robert S. Strichartz, Cornell UniversityReceived his Ph.D. (1966) from Princeton University and is currently teaches mathematics at Cornell University. Research interests cover a wide range of topics in analysis, including harmonic analysis, partial differential equations, analysis on Lie groups and manifolds, integral geometry, wavelets and fractals.Robert's early work using methods of harmonic analysis to obtain fundamental estimates for linear wave equations has played an important role in recent developments in the theory of nonlinear wave equations. His work on fractals began with the study of self-similar measures and their Fourier transforms. More recentlyhis have been concentrating on a theory of differential equationson fractals created by Jun Kigami. Much of this work has been done in collaboration with undergraduate students through a summer Research Experiences for Undergraduates (REU) program at Cornell thathe directs.Robert wrote an expository article Analysis On Fractals, Notices of the AMS 46 (1999), 1199 - 1208 explaining the basic ideas in this subject area and the connections with other areas of mathematics.

מידע ביבליוגרפי

כותרתThe Way of Analysis
Jones and Bartlett books in mathematics
מאתRobert S. Strichartz
מהדורהמאויר, מהדורה מעודכנת
הוצאהJones & Bartlett Learning, 2000
ISBN0763714976, 9780763714970
אורך739 עמודים
  
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