{"product_id":"linear-ordinary-differential-equations-paperback-softback-9780898713886","title":"Linear Ordinary Differential Equations (Paperback \/ softback) 9780898713886","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLinear Ordinary Differential Equations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA thorough development of the main topics in linear differential equations with applications, examples, and exercises illustrating each topic.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eEarl A.  Coddington (Author), Robert Carlson (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780898713886, Society for Industrial and Applied Mathematics\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 1 January 1987\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e348 pages\u003cbr\u003e25.3 x 17.8 x 1.5 cm, 0.636 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eLinear Ordinary Differential Equations, a text for advanced undergraduate or beginning graduate students, presents a thorough development of the main topics in linear differential equations. A rich collection of applications, examples, and exercises illustrates each topic. The authors reinforce students' understanding of calculus, linear algebra, and analysis while introducing the many applications of differential equations in science and engineering. Three recurrent themes run through the book. The methods of linear algebra are applied directly to the analysis of systems with constant or periodic coefficients and serve as a guide in the study of eigenvalues and eigenfunction expansions. The use of power series, beginning with the matrix exponential function leads to the special functions solving classical equations. Techniques from real analysis illuminate the development of series solutions, existence theorems for initial value problems, the asymptotic behavior solutions, and the convergence of eigenfunction expansions.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface. 1. Simple Applications. Introduction\u003cbr\u003e Compartment systems\u003cbr\u003e Springs and masses\u003cbr\u003e Electric circuits\u003cbr\u003e Notes\u003cbr\u003e Exercises\u003cbr\u003e 2. Properties of Linear Systems. Introduction\u003cbr\u003e Basic linear algebra\u003cbr\u003e First-order systems\u003cbr\u003e Higher-order equations\u003cbr\u003e Notes\u003cbr\u003e Exercises\u003cbr\u003e 3. Constant Coefficients. Introduction\u003cbr\u003e Properties of the exponential of a matrix\u003cbr\u003e Nonhomogeneous systems\u003cbr\u003e Structure of the solution space\u003cbr\u003e The Jordan canonical form of a matrix\u003cbr\u003e The behavior of solutions for large t\u003cbr\u003e Higher-order equations\u003cbr\u003e Exercises\u003cbr\u003e 4. Periodic Coefficients. Introduction\u003cbr\u003e Floquet's theorem\u003cbr\u003e The logarithm of an invertible matrix\u003cbr\u003e Multipliers\u003cbr\u003e The behavior of solutions for large t\u003cbr\u003e First-order nonhomogeneous systems\u003cbr\u003e Second-order homogeneous equations\u003cbr\u003e Second-order nonhomogeneous equations\u003cbr\u003e Notes\u003cbr\u003e Exercises\u003cbr\u003e 5. Analytic Coefficients. Introduction\u003cbr\u003e Convergence\u003cbr\u003e Analytic functions\u003cbr\u003e First-order linear analytic systems\u003cbr\u003e Equations of order n\u003cbr\u003e The Legendre equation and its solutions\u003cbr\u003e Notes\u003cbr\u003e Exercises\u003cbr\u003e 6. Singular Points. Introduction\u003cbr\u003e Systems of equations with singular points\u003cbr\u003e Single equations with singular points\u003cbr\u003e Infinity as a singular point\u003cbr\u003e Notes\u003cbr\u003e Exercises\u003cbr\u003e 7. Existence and Uniqueness. Introduction\u003cbr\u003e Convergence of successive approximations\u003cbr\u003e Continuity of solutions\u003cbr\u003e More general linear equations\u003cbr\u003e Estimates for second-order equations\u003cbr\u003e Notes\u003cbr\u003e Exercises\u003cbr\u003e 8. Eigenvalue Problems. Introduction\u003cbr\u003e Inner products\u003cbr\u003e Boundary conditions and operators\u003cbr\u003e Eigenvalues\u003cbr\u003e Nonhomogeneous boundary value problems\u003cbr\u003e Notes\u003cbr\u003e Exercises\u003cbr\u003e 9. Eigenfunction Expansions. Introduction\u003cbr\u003e Selfadjoint integral operators\u003cbr\u003e Eigenvalues for Green's operator\u003cbr\u003e Convergence of eigenfunction expansions\u003cbr\u003e Extensions of the expansion results\u003cbr\u003e Notes\u003cbr\u003e Exercises\u003cbr\u003e 10. Control of Linear Systems. Introduction\u003cbr\u003e Convex sets\u003cbr\u003e Control of general linear systems\u003cbr\u003e Constant coefficient equations\u003cbr\u003e Time-optimal control\u003cbr\u003e Notes\u003cbr\u003e Exercises\u003cbr\u003e Bibliography.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Applied mathematics [\u003ca title=\"See our other books on Applied mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Applied%20mathematics%20%5BPBW%5D%22\"\u003ePBW\u003c\/a\u003e], Differential calculus \u0026amp; equations [\u003ca title=\"See our other books on Differential calculus \u0026amp; equations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Differential%20calculus%20\u0026amp;%20equations%20%5BPBKJ%5D%22\"\u003ePBKJ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Society for Industrial and Applied Mathematics","offers":[{"title":"Brand New","offer_id":52509194912024,"sku":"9780898713886","price":79.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780898713886I.jpg?v=1786497201","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/linear-ordinary-differential-equations-paperback-softback-9780898713886","provider":"Freshly Printed Books","version":"1.0","type":"link"}