SpringerBriefs in Physics: Differential and Difference Equations : A Comparison of Methods of Solution by Leonard C. Maximon read DJV, EPUB, TXT
9783319297354 331929735X This book provides a detailed comparison of methods ofsolution of linear differential and linear difference equations, allowing thereader to understand difference equations from the more familiar perspective ofdifferential equations. Throughout thebook the emphasis is on providing the detail that would facilitate theapplication of these methods to particular problems, including the solution offirst and second order equations, asymptotic solutions, Green's function,generating functions, integral transforms, Sturm-Liouvile theory, and theclassical functions of mathematical physics. In presenting a given topic, the attempt has beenmade to follow the analysis for differential equations by the analogousanalysis for difference equations. The book is unique in its treatment of the two subjects,difference equations and differential equations. These are generally treated separately, withonly a brief reference to the similarity of the respective analyses. The book aims to make difference equationsmore understandable to the broad readership in engineering and the physicalsciences for whom differential equations are familiar tools of the trade., This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations - variation of constants, reduction of order, Laplace transforms and generating functions - bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green s functions and the associated initial and boundary conditions is presented for differential and difference equations of both arbitrary and second order. A dictionary of difference equations with polynomial coefficients provides a unique compilation of second order difference equations obeyed by the special functions of mathematical physics. Appendices augmenting the text include, in particular, a proof of Cramer s rule, a detailed consideration of the role of the superposition principal in the Green s function, and a derivation of the inverse of Laplace transforms and generating functions of particular use in the solution of second order linear differential and difference equations with linear coefficients. "
9783319297354 331929735X This book provides a detailed comparison of methods ofsolution of linear differential and linear difference equations, allowing thereader to understand difference equations from the more familiar perspective ofdifferential equations. Throughout thebook the emphasis is on providing the detail that would facilitate theapplication of these methods to particular problems, including the solution offirst and second order equations, asymptotic solutions, Green's function,generating functions, integral transforms, Sturm-Liouvile theory, and theclassical functions of mathematical physics. In presenting a given topic, the attempt has beenmade to follow the analysis for differential equations by the analogousanalysis for difference equations. The book is unique in its treatment of the two subjects,difference equations and differential equations. These are generally treated separately, withonly a brief reference to the similarity of the respective analyses. The book aims to make difference equationsmore understandable to the broad readership in engineering and the physicalsciences for whom differential equations are familiar tools of the trade., This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations - variation of constants, reduction of order, Laplace transforms and generating functions - bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green s functions and the associated initial and boundary conditions is presented for differential and difference equations of both arbitrary and second order. A dictionary of difference equations with polynomial coefficients provides a unique compilation of second order difference equations obeyed by the special functions of mathematical physics. Appendices augmenting the text include, in particular, a proof of Cramer s rule, a detailed consideration of the role of the superposition principal in the Green s function, and a derivation of the inverse of Laplace transforms and generating functions of particular use in the solution of second order linear differential and difference equations with linear coefficients. "