{"product_id":"real-analysis-9780821836705","title":"Real Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSuitable for undergraduates studying real analysis, this book presents the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in $\\mathbb{R}^n$. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I: Real numbers and limits: Numbers and logic Infinity Sequences Functions and limits Part II: Topology: Open and closed sets Continuous functions Composition of functions Subsequences Compactness Existence of maximum Uniform continuity Connected sets and the intermediate value theorem The Cantor set and fractals Part III: Calculus: The derivative and the mean value theorem The Riemann integral The fundamental theorem of calculus Sequences of functions The Lebesgue theory Infinite series $\\sum a_n$ Absolute convergence Power series Fourier series Strings and springs Convergence of Fourier series The exponential function Volumes of $n$-balls and the gamma function Part IV: Metric spaces: Metric spaces Analysis on metric spaces Compactness in metric spaces Ascoli's theorem Partial solutions to exercises Greek letters Index.","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50577672864087,"sku":"9780821836705","price":46.75,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780821836705.jpg?v=1746096120","url":"https:\/\/bookcurl.com\/products\/real-analysis-9780821836705","provider":"Book Curl","version":"1.0","type":"link"}