{"product_id":"quaternionic-eulerian-calculus","title":"Quaternionic Eulerian Calculus","description":"\u003cp\u003eQuaternionic Eulerian Calculus (QEC) is a new field of calculus wherein differential and integral calculus  are based upon Euler's formula.  Given the definition of the limit, as defined and proven by the delta-epsilon proof, the Newtonian derivative, f'(x), is not and cannot be a limit as defined.  The formal delta-epsilon definition of a limit proscribes precision. The derivative, contrarily, obtains a precise value symbolically. As a limit, it is proven that  a precise  value of the difference quotient is obtained when h=versine=0,  absent any reliance upon the delta-epsilon proof.  It is also proven  that f'(x) is an instantaneous center of revolution, that f'(x) is equivalent to the  quaternion rotator operator, *h[ ]h, and lastly that i=square root of -1, is a quaternion and  functions as a derivative. These concepts are the essence of QEC. Several practical applications are provided including a solution to the Riemann Hypothesis and a QEC analysis of DNA translation.\u003c\/p\u003e","brand":"BooksWholesale","offers":[{"title":"Hardcover","offer_id":44598096527521,"sku":"sephard1934","price":54.88,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0462\/1120\/3233\/files\/1nznr8zk-front-shortedge-384.jpg?v=1725411001","url":"https:\/\/bookswholesale.myshopify.com\/products\/quaternionic-eulerian-calculus","provider":"BooksWholesale","version":"1.0","type":"link"}