A Treatise on Differential Equations and on the Calculus of Finite Differences (Classic Reprint)

Ts. vii FINITE DIFFERENCES. SECTION I. DIRECT METHOD OF DIFFERENCES. ABT. PAGE 16. Definitions and Principles 17 17. Differences of Explicit Functions 418 26. Relations between the successiye Values and theD ifferences of a Function 827 32. Generating Functions 13 33 39. Separation of theS ymbols ofO peration from those of Quantity ,18 SECTION II. inverse method of differences. 40 63. Integration of Explicit Functions 24 64 71. Numbers of Bernouilli 39 SECTION III. equations of differences. 72, 73. Origin and Nature of Equations of Differences 47 74. Linear Equations of Differences of the First Order 48 75. Indirect Integrals of Equations of Differenced 51 76 85. Linear Equations of Differences of allO rders 53 86 87. Certain Equations reducible to Linear Equations.
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