A Treatise on the Calculus of Finite Differences: THE APPROXIMATE SUMMATION OF SERIES

Preface to the first edition Preface to the second edition 1. Nature of the calculus of finite differences 2. Direct theorems of finite differences 3. On interpolation, and mechanical quadrature 4. Finite integration, and the summation of series 5. The approximate summation of series 6. Bernoulli's numbers, and factorial coefficients 7. Convergency and divergency of series 8. Exact theorems 9. Difference-equations of the first order 10. General theory of the solutions of difference- and differential equations of the first order 11. Linear difference-equations with constant coefficients 12. Miscellaneous propositions and equations. Simultaneous equations 13. Linear equations with variable coefficients. Symbolical and general methods 14. Mixed and partial difference-equations 15. Of the calculus of functions 16. Geometrical applications Answers to the exercises.