Princeton Lectures in Analysis: Difference between revisions

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{{Short description|Series of four mathemeticsmathematics textbooks}}{{italic title}}

{{Infobox book series

| name = ''Princeton Lectures in Analysis''

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''Complex Analysis'' treats the standard topics of a course in complex variables as well as several applications to other areas of mathematics.<ref name=fefferman/><ref name=shiu/> The chapters cover the [[complex plane]], [[Cauchy's integral theorem]], [[meromorphic function]]s, connections to Fourier analysis, [[entire function]]s, the [[gamma function]], the [[Riemann zeta function]], [[conformal map]]s, [[elliptic function]]s, and [[theta function]]s.<ref name=ss2>Stein & Shakarchi, ''Complex Analysis''.</ref>

''Real Analysis'' begins with [[measure theory]], Lebesgue integration, and [[differentiation (mathematics)|differentiation]] in [[Euclidean space]]. It then covers [[Hilbert space]]s before returning to measure and integration in the context of [[Measure space|abstract measure spaces]]. It concludes with a chapter on [[Hausdorff measure]] and [[fractal]]s.<ref name=ss3>Stein & Shakarchi, ''Real Analysis''.</ref>

''Functional Analysis'' has chapters on several advanced topics in analysis: [[Lp space|L^''p'' spaces]], [[Distribution (mathematics)|distributions]], the [[Baire category theorem]], [[probability theory]] including [[Brownian motion]], [[several complex variables]], and [[oscillatory integral]]s.<ref name=ss4>Stein & Shakarchi, ''Functional Analysis''.</ref>