{"product_id":"differential-equations-fourier-series-and-hilbert-spaces-9783111294858","title":"Differential Equations, Fourier Series, and Hilbert Spaces","description":"\u003cp\u003eThis book is intended to be used as a rather informal, and surely not complete, textbook on the subjects indicated in the title. It collects my Lecture Notes held during three academic years at the University of Siena for a one semester course on \"Basic Mathematical Physics\", and is organized as a short presentation of few important points on the arguments indicated in the title. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eIt aims at completing the students' basic knowledge on Ordinary Differential Equations (ODE) - dealing in particular with those of higher order - and at providing an elementary presentation of the Partial Differential Equations (PDE) of Mathematical Physics, by means of the classical methods of separation of variables and Fourier series. For a reasonable and consistent discussion of the latter argument, some elementary results on Hilbert spaces and series expansion in othonormal vectors are treated with some detail in Chapter 2. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003ePrerequisites for a satisfactory reading of the present Notes are not only a course of Calculus for functions of one or several variables, but also a course in Mathematical Analysis where - among others - some basic knowledge of the topology of normed spaces is supposed to be included. For the reader's convenience some notions in this context are explicitly recalled here and there, and in particular as an Appendix in Section 1.4. An excellent reference for this general background material is W. Rudin's classic Principles of Mathematical Analysis\u003cem\u003e. On the other hand, a complete discussion of the results on ODE and PDE that are here just sketched are to be found in other books, specifically and more deeply devoted to these subjects, some of which are listed in the Bibliography.\u003c\/em\u003e \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eIn conclusion and in brief, my hope is that the present Notes can serve as a second quick reading on the theme of ODE, and as a first introductory reading on Fourier series, Hilbert spaces, and PDE \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=AUTH-16282071\"\u003eRaffaele Chiappinelli\u003c\/a\u003e\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e de Gruyter\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/04\/2023\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 220\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.79lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.61h x 6.69w x 0.47d\u003cbr\u003e\u003cb\u003eISBN13:\u003c\/b\u003e 9783111294858\u003cbr\u003e\u003cb\u003eISBN10:\u003c\/b\u003e 3111294854\u003cbr\u003e\u003cb\u003eBISAC Categories:\u003c\/b\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-MAT\"\u003eMathematics\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-MAT007010\"\u003eDifferential Equations | Ordinary\u003c\/a\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-MAT\"\u003eMathematics\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-MAT003000\"\u003eApplied\u003c\/a\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-SCI\"\u003eScience\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-SCI040000\"\u003ePhysics | Mathematical \u0026amp; Computational\u003c\/a\u003e\u003cbr\u003e","brand":"de Gruyter","offers":[{"title":"Default Title","offer_id":44379579089133,"sku":"9783111294858","price":87.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0550\/8097\/6621\/products\/img_5736a54d-6c19-40bf-826a-4bfef3954611.jpg?v=1699197179","url":"https:\/\/sureshotbooks.com\/products\/differential-equations-fourier-series-and-hilbert-spaces-9783111294858","provider":"SureShot Books Publishing LLC","version":"1.0","type":"link"}