{"product_id":"9783031995422","title":"Springer Undergraduate Mathematics Series","description":"\u003ch1\u003eSpringer Undergraduate Mathematics Series\u003c\/h1\u003e \u003ch2\u003eMatthews, Paul C.\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book introduces qualitative methods for understanding differential equations, especially when analytical solutions are not possible. Aimed at second-year undergraduate students in mathematics or science, it assumes prior knowledge of calculus, linear algebra, and curve sketching. The book focuses on phase plane methods for second-order differential equations, supported by earlier sections on analytical techniques and phase lines for first-order equations. The later chapters explore bifurcation theory and chaos. Emphasizing application over theory, the book includes diagrams, worked examples, and exercises, with minimal use of formal proofs.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2025-09-27\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783031995422\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-031-99543-9\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 235\u003c\/p\u003e ","brand":"Springer Nature Switzerland","offers":[{"title":"Default Title","offer_id":44343464919180,"sku":"9783031995422","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783031995422.jpg?v=1775730955","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783031995422","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}