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.
General
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