{"product_id":"fundamentals-of-advanced-mathematics-v2-field-extensions-topology-and-topological-vector-spaces-functional-spaces-and-sheaves-hardback-9781785482496","title":"Fundamentals of Advanced Mathematics V2; Field extensions, topology and topological vector spaces, functional spaces, and sheaves (Hardback) 9781785482496","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eFundamentals of Advanced Mathematics V2\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eField extensions, topology and topological vector spaces, functional spaces, and sheaves\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003e\u003cp\u003eExplains mathematical notions and results that are essential for modern systems theory, robotics and several branches of physics\u003c\/p\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eHenri Bourles (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781785482496, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 17 January 2018\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e360 pages\u003cbr\u003e22.9 x 15.1 x 2.5 cm, 0.7 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\"As with the first volume, I’m not sure I see this book having extensive use as a textbook (not only because of the succinct exposition, but because the array of topics covered doesn’t match up with any standard course at the graduate level). However, also as with the first edition, the considerable amount of material included here and the efficient, concise way in which it is presented makes this book valuable as a reference.\" -\u003cb\u003e-MAA Reviews\u003c\/b\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eThe three volumes of this series of books, of which this is the second, put forward the mathematical elements that make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering.\u003c\/p\u003e  \u003cp\u003eWhereas the first volume focused on the formal conditions for systems of linear equations (in particular of linear differential equations) to have solutions, this book presents the approaches to finding solutions to polynomial equations and to systems of linear differential equations with varying coefficients.\u003c\/p\u003e  \u003cp\u003e\u003ci\u003eFundamentals of Advanced Mathematics, Volume 2: Field Extensions, Topology and Topological Vector Spaces, Functional Spaces, and Sheaves \u003c\/i\u003ebegins with the classical Galois theory and the theory of transcendental field extensions. Next, the differential side of these theories is treated, including the differential Galois theory (Picard-Vessiot theory of systems of linear differential equations with time-varying coefficients) and differentially transcendental field extensions. The treatment of analysis includes topology (using both filters and nets), topological vector spaces (using the notion of disked space, which simplifies the theory of duality), and the radon measure (assuming that the usual theory of measure and integration is known).\u003c\/p\u003e  \u003cp\u003eIn addition, the theory of sheaves is developed with application to the theory of distributions and the theory of hyperfunctions (assuming that the usual theory of functions of the complex variable is known). This volume is the prerequisite to the study of linear systems with time-varying coefficients from the point-of-view of algebraic analysis and the algebraic theory of nonlinear systems.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e1. Field Extensions and Differential Field Extensions 2. General Topology 3. Topological Vector Spaces 4. Measure and Integration, Function Spaces 5. Sheaves \u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Stochastics [\u003ca title=\"See our other books on Stochastics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Stochastics%20%5BPBWL%5D%22\"\u003ePBWL\u003c\/a\u003e], Probability \u0026amp; statistics [\u003ca title=\"See our other books on Probability \u0026amp; statistics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Probability%20\u0026amp;%20statistics%20%5BPBT%5D%22\"\u003ePBT\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"ISTE Press - Elsevier","offers":[{"title":"Default Title","offer_id":46651736391960,"sku":"9781785482496","price":113.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781785482496_4f8c43c4-e649-4515-a4a3-6704b3dbae00.jpg?v=1695018592","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/fundamentals-of-advanced-mathematics-v2-field-extensions-topology-and-topological-vector-spaces-functional-spaces-and-sheaves-hardback-9781785482496","provider":"Freshly Printed Books","version":"1.0","type":"link"}