Author | Goldstine, Herman H. author |
---|---|
Title | A History of Numerical Analysis from the 16th through the 19th Century [electronic resource] / by Herman H. Goldstine |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1977 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-9472-3 |
Descript | XIV, 350 p. online resource |
1. The Sixteenth and Early Seventeenth Centuries -- 1.1. Introduction -- 1.2. Napier and Logarithms -- 1.3. Briggs and His Logarithms -- 1.4. Bรผrgi and His Antilogarithms -- 1.5. Interpolation -- 1.6. Vieta and Briggs -- 1.7. Kepler -- 2. The Age of Newton -- 2.1. Introduction -- 2.2. Logarithms and Finite Differences -- 2.3. Trigonometric Tables -- 2.4. The Newton-Raphson and Other Iterative Methods -- 2.5. Finite Differences and Interpolation -- 2.6. Maclaurin on the Euler-Maclaurin Formula -- 2.7. Stirling -- 2.8. Leibniz -- 3. Euler and Lagrange -- 3.1. Introduction -- 3.2. Summation of Series -- 3.3. Euler on the Euler-Maclaurin Formula -- 3.4. Applications of the Summation Formula -- 3.5. Euler on Interpolation -- 3.6. Lunar Theory -- 3.7. Lagrange on Difference Equations -- 3.8. Lagrange on Functional Equations -- 3.9. Lagrange on Fourier Series -- 3.10. Lagrange on Partial Difference Equations -- 3.11. Lagrange on Finite Differences and Interpolation -- 3.12. Lagrange on Hidden Periodicities -- 3.13. Lagrange on Trigonometric Interpolation -- 4. Laplace, Legendre, and Gauss -- 4.1. Introduction -- 4.2. Laplace on Interpolation -- 4.3. Laplace on Finite Differences -- 4.4. Laplace Summation Formula -- 4.5. Laplace on Functional Equations -- 4.6. Laplace on Finite Sums and Integrals -- 4.7. Laplace on Difference Equations -- 4.8. Laplace Transforms -- 4.9. Method of Least Squares -- 4.10. Gauss on Least Squares -- 4.11. Gauss on Numerical Integration -- 4.12. Gauss on Interpolation -- 4.13. Gauss on Rounding Errors -- 5. Other Nineteenth Century Figures -- 5.1. Introduction -- 5.2. Jacobi on Numerical Integration -- 5.3. Jacobi on the Euler-Maclaurin Formula -- 5.4. Jacobi on Linear Equations -- 5.5. Cauchy on Interpolation -- 5.6. Cauchy on the Newton-Raphson Method -- 5.7. Cauchy on Operational Methods -- 5.8. Other Nineteenth Century Results -- 5.9. Integration of Differential Equations -- 5.10. Successive Approximation Methods -- 5.11. Hermite -- 5.12. Sums