{"product_id":"perfect-form-variational-principles-methods-and-applications-in-elementary-physics-paperback","title":"Perfect Form: Variational Principles, Methods, and Applications in Elementary Physics - Paperback","description":"\u003cp\u003eby \u003cb\u003eDon S. Lemons\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eWhat does the path taken by a ray of light share with the trajectory of a thrown baseball and the curve of a wheat stalk bending in the breeze? Each is the subject of a different study yet all are optimal shapes; light rays minimize travel time while a thrown baseball minimizes action. All natural curves and shapes, and many artificial ones, manifest such \"perfect form\" because physical principles can be expressed as a statement requiring some important physical quantity to be mathematically maximum, minimum, or stationary. \u003ci\u003ePerfect Form\u003c\/i\u003e introduces the basic \"variational\" principles of classical physics (least time, least potential energy, least action, and Hamilton's principle), develops the mathematical language most suited to their application (the calculus of variations), and presents applications from the physics usually encountered in introductory course sequences. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e The text gradually unfolds the physics and mathematics. While other treatments postulate Hamilton's principle and deduce all results from it, \u003ci\u003ePerfect Form\u003c\/i\u003e begins with the most plausible and restricted variational principles and develops more powerful ones through generalization. One selection of text and problems even constitutes a non-calculus of variations introduction to variational methods, while the mathematics more generally employed extends only to solving simple ordinary differential equations. \u003ci\u003ePerfect Form\u003c\/i\u003e is designed to supplement existing classical mechanics texts and to present variational principles and methods to students who approach the subject for the first time.\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003eWhat does the path taken by a ray of light share with the trajectory of a thrown baseball and the curve of a wheat stalk bending in the breeze? Each is the subject of a different study yet all are optimal shapes; light rays minimize travel time while a thrown baseball minimizes action. All natural curves and shapes, and many artificial ones, manifest such \"perfect form\" because physical principles can be expressed as a statement requiring some important physical quantity to be mathematically maximum, minimum, or stationary. Perfect Form introduces the basic \"variational\" principles of classical physics (least time, least potential energy, least action, and Hamilton's principle), develops the mathematical language most suited to their application (the calculus of variations), and presents applications from the physics usually encountered in introductory course sequences.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cb\u003eDon S. Lemons\u003c\/b\u003e is Associate Professor of Physics at Bethel College of North Newton, Kansas.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 136\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.33 x 9.28 x 6.14 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e March 23, 1997\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42723351887935,"sku":"9780691026633","price":139.54,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/b982af86a531d313ba24acc2bf184eef.webp?v=1765098874","url":"https:\/\/dhlswag.com\/products\/perfect-form-variational-principles-methods-and-applications-in-elementary-physics-paperback","provider":"BBB","version":"1.0","type":"link"}