{"product_id":"9780412233401","title":"Functions of several variables","description":"\u003ch1\u003eFunctions of several variables\u003c\/h1\u003e \u003ch2\u003eCraven, B.\u003c\/h2\u003e \u003cp\u003eThis book is aimed at mathematics students, typically in the second year of a university course. The first chapter, however, is suitable for first-year students. Differentiable functions are treated initially from the standpoint of approximating a curved surface locally by a fiat surface. This enables both geometric intuition, and some elementary matrix algebra, to be put to effective use. In Chapter 2, the required theorems - chain rule, inverse and implicit function theorems, etc- are stated, and proved (for n variables), concisely and rigorously. Chapter 3 deals with maxima and minima, including problems with equality and inequality constraints. The chapter includes criteria for discriminating between maxima, minima and saddlepoints for constrained problems; this material is relevant for applications, but most textbooks omit it. In Chapter 4, integration over areas, volumes, curves and surfaces is developed, and both the change-of-variable formula, and the Gauss-Green-Stokes set of theorems are obtained. The integrals are defined with approximative sums (ex­ pressed concisely by using step-functions); this preserves some geometrical (and physical) concept of what is happening. Consequent on this, the main ideas of the 'differential form' approach are presented, in a simple form which avoids much of the usual length and complexity. Many examples and exercises are included.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1981-12-10\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9780412233401\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-94-010-9347-7\u003c\/p\u003e \u003cp\u003eDimensions: 210cm x148cm\u003c\/p\u003e \u003cp\u003ePages: 138\u003c\/p\u003e ","brand":"Springer Netherlands","offers":[{"title":"Default Title","offer_id":44448497074316,"sku":"9780412233401","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780412233401.jpg?v=1775791168","url":"https:\/\/lateknightbooks.com\/products\/9780412233401","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}