This pertains to Laguerre's equation xy " + ( 1 – x ) y ' + my = 0 . ( a ) Obtain a recursion formula for a series ... The resulting polynomials , multiplied by a constant to give y ( 0 ) m !, are the Laguerre polynomials Lm ( x ) .
The summation in (43.37) is now the same as the right side of L. (c) of (43.2). B. Integral Property of Laguerre Polynomials. Theorem 43.4. Let Losa), L1(c), L2(a), . . . , be Laguerre polynomial solutions of (43.1).
This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us.
Used in undergraduate classrooms across the USA, this is a clearly written, rigorous introduction to differential equations and their applications.
Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; further developments in the ...
This book compiles the most widely applicable methods for solving and approximating differential equations. as well as numerous examples showing the methods use.
Detailed, fully worked-out solutions to problems The inside scoop on first, second, and higher order differential equations A wealth of advanced techniques, including power series THE DUMMIES WORKBOOK WAY Quick, refresher explanations Step ...
A thorough and systematic first course in elementary differential equations for undergraduates in mathematics and science, with many exercises and problems (with answers).
This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more.
In addition to minor corrections and updates throughout, this new edition contains materials on higher order Melnikov functions and the bifurcation of limit cycles for planar systems of differential equations, including new sections on ...
The author developed and used this book to teach Math 286 and Math 285 at the University of Illinois at Urbana-Champaign. The author also taught Math 20D at the University of California, San Diego with this book.