Table of Contents

1. Introduction 2. Displacement-Symbols and Differences 3. Divided Differences 4. Interpolation-Formulas 5. Some Applications 6. Factorial Coefficients 7. Numerical Differentiation 8. Construction of Tables 9. Inverse Interpolation 10. Elementary Methods of Summation 11. Repeated Summation 12. Laplace's and Gauss's Summation-Formulas 13. Bernoulli's Polynomials 14. Euler's Summation-Formula 15. Lubbock's and Woolhouse's Formulas 16. Mechanical Quadrature 17. Numerical Integration of Differential Equations 18. The Calculus of Symbols 19. Interpolation with Several Variables 20. Mechanical Cubature Appendix