{"product_id":"introduction-to-real-analysis-isbn-9780471853916","title":"Introduction to Real Analysis","description":"Assuming minimal background on the part of students, this text gradually develops the principles of basic real analysis and presents the background necessary to understand applications used in such disciplines as statistics, operations research, and engineering. The text presents the first elementary exposition of the gauge integral and offers a clear and thorough introduction to real numbers, developing topics in n-dimensions, and functions of several variables. Detailed treatments of Lagrange multipliers and the Kuhn-Tucker Theorem are also presented. The text concludes with coverage of important topics in abstract analysis, including the Stone-Weierstrass Theorem and the Banach Contraction Principle. Preliminaries.\u003cbr\u003e \u003cbr\u003e Real Numbers.\u003cbr\u003e \u003cbr\u003e Sequences.\u003cbr\u003e \u003cbr\u003e Infinite Series.\u003cbr\u003e \u003cbr\u003e Euclidean Spaces.\u003cbr\u003e \u003cbr\u003e Limits of Functions.\u003cbr\u003e \u003cbr\u003e Continuity and Uniform Continuity.\u003cbr\u003e \u003cbr\u003e Sequences of Functions.\u003cbr\u003e \u003cbr\u003e The Riemann Integral Reviewed.\u003cbr\u003e \u003cbr\u003e The Gauge Integral.\u003cbr\u003e \u003cbr\u003e The Gauge Integral Over Unbounded Intervals.\u003cbr\u003e \u003cbr\u003e Convergence Theorems.\u003cbr\u003e \u003cbr\u003e Multiple Integrals.\u003cbr\u003e \u003cbr\u003e Convolution and Approximation.\u003cbr\u003e \u003cbr\u003e Metric Spaces.\u003cbr\u003e \u003cbr\u003e Topology in Metric Spaces.\u003cbr\u003e \u003cbr\u003e Continuity.\u003cbr\u003e \u003cbr\u003e Complete Metric Spaces.\u003cbr\u003e \u003cbr\u003e Contraction Mappings.\u003cbr\u003e \u003cbr\u003e The Baire Category Theorem.\u003cbr\u003e \u003cbr\u003e Compactness.\u003cbr\u003e \u003cbr\u003e Connectedness.\u003cbr\u003e \u003cbr\u003e The Stone-Weierstrass Theorem.\u003cbr\u003e \u003cbr\u003e Differentiation of Vector-valued Functions.\u003cbr\u003e \u003cbr\u003e Mapping Theorems.\u003cbr\u003e \u003cbr\u003e Bibliography.\u003cbr\u003e \u003cbr\u003e Index.  \u003cp\u003eJohn DePree and Charles Swartz are the authors of Introduction to Real Analysis, published by Wiley.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989466038501,"sku":"NP9780471853916","price":202.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471853916.jpg?v=1761784211","url":"https:\/\/k12savings.com\/es\/products\/introduction-to-real-analysis-isbn-9780471853916","provider":"K12savings","version":"1.0","type":"link"}