{"product_id":"an-introduction-to-analysis-9781032021867","title":"An Introduction to Analysis","description":"\u003cp\u003e • Author(s): James R. Kirkwood\u003cbr\u003e • Publisher: Taylor \u0026amp; Francis\u003cbr\u003e • Publisher Imprint: Chapman Hall\u003cbr\u003e • Subject: Mathematics and Statistics\u003cbr\u003e • BISAC: Mathematical Analysis\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe third edition of this widely popular textbook is authored by a master teacher.\u003cb\u003e \u003c\/b\u003eThis book provides a mathematically rigorous introduction to analysis of real-valued functions of one variable. This intuitive, student-friendly text is written in a manner that will help to ease the transition from primarily computational to primarily theoretical mathematics. \u003c\/p\u003e\u003cp\u003eThe material is presented clearly and as intuitive as possible while maintaining mathematical integrity. The author supplies the ideas of the proof and leaves the write-up as an exercise. The text also states why a step in a proof is the reasonable thing to do and which techniques are recurrent.\u003c\/p\u003e\u003cp\u003eExamples, while no substitute for a proof, are a valuable tool in helping to develop intuition and are an important feature of this text. Examples can also provide a vivid reminder that what one hopes might be true is not always true. \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eFeatures of the Third Edition: \u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eBegins with a discussion of the axioms of the real number system.\u003c\/li\u003e \u003c\/ul\u003e\u003cul\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eThe limit is introduced via sequences.\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eExamples motivate what is to come, highlight the need for hypothesis in a theorem, and make abstract ideas more concrete.\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eA new section on the Cantor set and the Cantor function. \u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eAdditional material on connectedness.\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eExercises range in difficulty from the routine \"getting your feet wet\" types of problems to the moderately challenging problems.\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eTopology of the real number system is developed to obtain the familiar properties of continuous functions.\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eSome exercises are devoted to the construction of counterexamples. \u003c\/li\u003e \u003c\/ul\u003e\u003cp\u003eThe author presents the material to make the subject understandable and perhaps exciting to those who are beginning their study of abstract mathematics.\u003c\/p\u003e\u003cp\u003eTable of Contents\u003c\/p\u003e\u003cp\u003ePreface\u003c\/p\u003e\u003cp\u003eIntroduction\u003c\/p\u003e\u003col\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eThe Real Number System\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eSequences of Real Numbers\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eTopology of the Real Numbers\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eContinuous Functions\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eDifferentiation\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eIntegration\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eSeries of Real Numbers\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eSequences and Series of Functions\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eFourier Series\u003c\/li\u003e \u003c\/ol\u003e\u003cp\u003eBibliography\u003c\/p\u003e\u003cp\u003eHints and Answers to Selected Exercises\u003c\/p\u003e\u003cp\u003eIndex\u003c\/p\u003e\u003cp\u003eBiography\u003c\/p\u003e\u003cp\u003eJames R. Kirkwood holds a Ph.D. from University of Virginia. He has authored fifteen, published mathematics textbooks on various topics including calculus, real analysis, mathematical biology and mathematical physics. His original research was in mathematical physics, and he co-authored the seminal paper in a topic now called Kirkwood-Thomas Theory in mathematical physics. During the summer, he teaches real analysis to entering graduate students at the University of Virginia. He has been awarded several National Science Foundation grants. His texts, \u003ci\u003eElementary\u003c\/i\u003e \u003ci\u003eLinear Algebra\u003c\/i\u003e, \u003ci\u003eLinear Algebra\u003c\/i\u003e, and \u003ci\u003eMarkov Processes, \u003c\/i\u003eare also published by CRC Press.\u003c\/p\u003e","brand":"Taylor \u0026 Francis","offers":[{"title":"Paperback","offer_id":45243337113751,"sku":"9781032021867","price":5117.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781032021867.webp?v=1769234351","url":"https:\/\/atlanticbooks.com\/products\/an-introduction-to-analysis-9781032021867","provider":"Atlantic Books","version":"1.0","type":"link"}