## Finite Difference EquationsComprehensive study focuses on use of calculus of finite differences as an approximation method for solving troublesome differential equations. Elementary difference operations; interpolation and extrapolation; modes of expansion of the solutions of nonlinear equations, applications of difference equations, difference equations associated with functions of two variables, more. Exercises with answers. 1961 edition. |

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### Contents

INTERPOLATION AND EXTRAPOLATION | 36 |

THE DETERMINATION OF DIFFERENCE EQUATIONS | 75 |

LINEAR DIFFERENCE AND FUNCTIONAL EQUATIONS WITH | 94 |

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### Common terms and phrases

absolutely convergent Accordingly algebra applications approximation arbitrary constants arbitrary function arbitrary unit periodic ascending powers asymptotic At(x Bernoulli polynomials boundary conditions calculated CALCULUS OF VARIATIONS coefficients column complementary function Consider corresponding derived determine difference equation y(x DIFFERENTIAL EQUATIONS elementary Example EXERCISES expansion expression for y(x extended differences factors follows form y(x formula functional equation Hence illustrate independent variable initial values inserting integer integral values interpolation INTRODUCTION J. P. Den Hartog limiting point line y(x linear difference equation linear equation mathematical method multiplying number of arbitrary obtain ORDINARY DIFFERENTIAL EQUATIONS original equation partial difference equation particular solution periodic function plane polynomial function positive integer problems range relation right-hand side rth order satisfies the equation sequence Show Solve the equation summation Taylor's theorem theorem theory transformation value of y(x xy(x yn+1 yn+l yn+t zero