Finite Difference Equations
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Specificatii
The calculus of finite differences is an area of mathematics
important to a broad range of professions, from physical science
and engineering to social sciences and statistics. This
comprehensive study, directed to advanced undergraduate-level
students, graduate students, and professionals, concentrates
primarily on how the calculus of finite differences may be used as
an approximation method for solving troublesome differential
equations.Stressing problem solving rather than pure mathematics,
the authors begin with elementary difference operations, treat
interpolation and extrapolation, the derivation of difference
equations, solution of linear difference equations with variable
and constant coefficients, and the properties of the general
difference equations. Chapter 5 develops the various modes of
expansion of the solutions of nonlinear equations and the
conditions under which these are valid. In addition, in Chapter 6,
there is the estimation of the eigenvalues that arise in connection
with linear difference equations, and the investigation of the
properties of the corresponding orthogonal functions in the form of
factorial series. The final two chapters treat applications of
difference equations, and the investigation of the properties of
the corresponding orthogonal functions in the form of factorial
series. The final two chapters treat applications of difference
equations and difference equations associated with functions of two
variables. Included are a number of exercises with answers.
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