{"title":"Bryan Rynne","description":null,"products":[{"product_id":"linear-functional-analysis-book-bryan-rynne-9781848000049","title":"Linear Functional Analysis","description":"This book provides an introduction to the ideas and methods of linear fu- tional analysis at a level appropriate to the ?nal year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the t- ory of metric spaces). Part of the development of functional analysis can be traced to attempts to ?nd a suitable framework in which to discuss di?erential and integral equations. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions de?ned on some set. In general, such a v- tor space is in?nite-dimensional. This leads to di?culties in that, although many of the elementary properties of ?nite-dimensional vector spaces hold in in?nite-dimensional vector spaces, many others do not. For example, in general in?nite-dimensionalvectorspacesthereisnoframeworkinwhichtomakesense of analytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now brie?y outline the contents of the book.","brand":"WoB","offers":[{"title":"GB \/ GOOD \/ INTERNAL","offer_id":49537001652497,"sku":"GOR008968768","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":49545829744913,"sku":"GOR006032956","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ GARDNERS","offer_id":49926801785105,"sku":"NGR9781848000049","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1848000049.jpg?v=1751123184"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-bryan-rynne.oembed","provider":"World of Books ","version":"1.0","type":"link"}