Newton–Cotes

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11: 33.7 Integral Representations

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12: Bibliography V

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Newton polyhedra and estimates of oscillatory integrals. Funkcional. Anal. i Priložen. 10 (3), pp. 13–38 (Russian).

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Notes:

English translation in Functional Anal. Appl. 18 (1976), pp. 175-196.

External Links:

ISSN 0374-1990, Document, MathReview (Helmut Hamm), ZentralBlatt

Referenced by:

§36.6.

Encodings:

BibTeX

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13: 4.45 Methods of Computation

… ►For $x\in [-1/\mathrm{e},\mathrm{\infty })$ the principal branch $\mathrm{Wp}\left(x\right)$ can be computed by solving the defining equation $W{\mathrm{e}}^W=x$ numerically, for example, by Newton’s rule (§3.8(ii)). …

14: 22.19 Physical Applications

… ►With appropriate scalings, Newton’s equation of motion for a pendulum with a mass in a gravitational field constrained to move in a vertical plane at a fixed distance from a fulcrum is … ►Classical motion in one dimension is described by Newton’s equation …

15: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►this being a matrix element of the resolvent $F(T)={\left(z-T\right)}^{-1}$, this being a key quantity in many parts of physics and applied math, quantum scattering theory being a simple example, see Newton (2002, Ch. 7). …See Newton (2002, §§7.1 and 7.3). … ►This representation has poles with residues ${\left|\widehat{f}({\lambda }_n)\right|}^2$ at the discrete eigenvalues and a branch cut along $[0,\mathrm{\infty })$ with discontinuity, from below to above the cut, $2\pi \mathrm{i}{\left|\widehat{f}(\lambda )\right|}^2$, as in (1.18.53), see Newton (2002, §7.1.1). …

16: Bibliography S

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A global Newton method for the zeros of cylinder functions. Numer. Algorithms 18 (3-4), pp. 259–276.

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External Links:

ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vi).

Encodings:

BibTeX

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