{"product_id":"foundations-of-mathematical-analysis-9780486477664","title":"Foundations of Mathematical Analysis","description":"\u003ch2\u003eFoundations of Mathematical Analysis - Comprehensive Modern Analysis Textbook\u003c\/h2\u003e\n\n\u003cp\u003eThis classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. Upper-level undergraduate students with a background in calculus will benefit from its teachings, along with beginning graduate students seeking a firm grounding in modern analysis.\u003c\/p\u003e\n\n\u003ch2\u003eSelf-Contained Curriculum Structure\u003c\/h2\u003e\n\n\u003cp\u003eA self-contained text, it presents the necessary background on the limit concept, and the first seven chapters could constitute a one-semester introduction to limits. Subsequent chapters discuss differential calculus of the real line, the Riemann-Stieltjes integral, sequences and series of functions, transcendental functions, inner product spaces and Fourier series, normed linear spaces and the Riesz representation theorem, and the Lebesgue integral.\u003c\/p\u003e\n\n\u003ch2\u003eExtensive Exercise Collection\u003c\/h2\u003e\n\n\u003cp\u003eSupplementary materials include an appendix on vector spaces and more than 750 exercises of varying degrees of difficulty. Hints and solutions to selected exercises, indicated by an asterisk, appear at the back of the book. This extensive problem set allows students to test their understanding and develop problem-solving skills across all major topics in modern analysis.\u003c\/p\u003e\n\n\u003ch2\u003eTopics Covered\u003c\/h2\u003e\n\n\u003cul\u003e\n\u003cli\u003eLimit concepts and foundational theory\u003c\/li\u003e\n\u003cli\u003eDifferential calculus of the real line\u003c\/li\u003e\n\u003cli\u003eRiemann-Stieltjes integral\u003c\/li\u003e\n\u003cli\u003eSequences and series of functions\u003c\/li\u003e\n\u003cli\u003eTranscendental functions\u003c\/li\u003e\n\u003cli\u003eInner product spaces and Fourier series\u003c\/li\u003e\n\u003cli\u003eNormed linear spaces and Riesz representation theorem\u003c\/li\u003e\n\u003cli\u003eLebesgue integral\u003c\/li\u003e\n\u003cli\u003eVector spaces (appendix)\u003c\/li\u003e\n\u003c\/ul\u003e\n\n\u003ch2\u003eIdeal for Advanced Mathematics Students\u003c\/h2\u003e\n\n\u003cp\u003eDesigned for upper-level undergraduate students with calculus background and beginning graduate students, this text provides the rigorous foundation needed for advanced work in mathematical analysis, functional analysis, and related fields. The Dover Publications edition offers exceptional value for students and self-learners building expertise in modern analysis.\u003c\/p\u003e\n\n\u003ch2\u003eAbout the Author\u003c\/h2\u003e\n\n\u003cp\u003eRichard Johnsonbaugh was a professor at DePaul University.\u003c\/p\u003e","brand":"Dover Publications","offers":[{"title":"Default Title","offer_id":50680629199122,"sku":"9780486477664","price":16.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0831\/4771\/8930\/files\/img_401db230-6fe8-4690-b603-60df2c7add3f.jpg?v=1734923491","url":"https:\/\/surprise-castle.myshopify.com\/products\/foundations-of-mathematical-analysis-9780486477664","provider":"Surprise Castle","version":"1.0","type":"link"}