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richardson c introduction calculus finite diff 1954

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Textbook in PDF and DJVU formats Preface Introduction Definitions and Notation Tables of Differences Difference Formulas Symbolic Operators Finite Integration and Applications Finite Integration Summation of Series More Advanced Methods of Integration A Integration by Parts B Undetermined Coefficients and Functions Stirling Numbers Bernoulli and Euler Polynomials Bernoulli Functions, P_n(x) Properties of the Polynomials, P_n(x) Bernoulli Polynomials, B_n(x), and Numbers Other Developments of the Bernoulli Functions Bernoulli Polynomials of the Second Kind Euler Polynomials Interpolation Approximate Integration Introduction Newton's Interpolation Formulas Formulas of Gauss, Stirling, and Bessel Equidistant Terms with Terms Missing Lagrange's Interpolation Formula Concluding Remarks on Interpolation Approximate Integration (a) The Trapezoidal Rule (b) Simpson's One-Third Rule (c) Simpson's Three-Eighths Rule (d) Weddle's Rule (e) The Euler-Maclaurin Sum Formula Beta and Gamma Functions Introduction The Gamma Function The Beta Function Illustrative Examples Difference Equations Introduction Solution of a Difference Equation Derivation of a Difference Equation Solution of Simple Difference Equations Linear Equations of Order One Linear Equations of Order n Linear Equations with Constant Coefficients Some Helpful Theorems Applications of Theorems Illustrative Examples Seliwanoff's Treatment of the Homogeneous Equation Multiple Roots in Auxiliary Equation by Operators Simultaneous Equations Rational Fractions The Psi Function Miscellaneous Equations The Linear Equation of Order Two Concluding Remarks Appendix I Mathematical Induction Appendix II Hyperbolic Functions Index

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Richardson C.An Introduction to the Calculus of Finite Diff 1954.djvu 1.2 MB
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richardson c introduction calculus finite diff 1954