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11: Bruce R. Miller

… ►There, he carried out research in non-linear dynamics and celestial mechanics, developing a specialized computer algebra system for high-order Lie transformations. …

12: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

§1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ► $V$ becomes a normed linear vector space. … ►

Bounded and Unbounded Linear Operators

… ► … ► …

13: 29.19 Physical Applications

… ►Roper (1951) solves the linearized supersonic flow equations. …

14: Mark J. Ablowitz

… ►for appropriate data they can be linearized by the Inverse Scattering Transform (IST) and they possess solitons as special solutions. …

15: Morris Newman

… ►Department of Commerce Gold Medal in 1966 for his work on algorithms for solving integral linear systems exactly by using congruence techniques. …

16: 3.8 Nonlinear Equations

… ►If $p=1$ and , then the convergence is said to be linear or geometric. … … ►

Regula Falsi

… ►Inverse linear interpolation (§3.3(v)) is used to obtain the first approximation: … ►This is useful when $f(z)$ satisfies a second-order linear differential equation because of the ease of computing $f^{\prime \prime }(z_n)$. …

17: Bibliography D

… ►

Complex zeros of linear combinations of spherical Bessel functions and their derivatives. SIAM J. Math. Anal. 4 (1), pp. 128–133.

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External Links:

ISSN 1095-7154, Document, MathReview (C. J. Bouwkamp), ZentralBlatt

Referenced by:

§10.58.

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Computing spectra of linear operators using the Floquet-Fourier-Hill method. J. Comput. Phys. 219 (1), pp. 296–321.

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External Links:

ISSN 0021-9991, MathReview, ZentralBlatt

Referenced by:

§22.11.

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Theta functions and non-linear equations. Uspekhi Mat. Nauk 36 (2(218)), pp. 11–80 (Russian).

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Notes:

With an appendix by I. M. Krichever. In Russian. English translation: Russian Math. Surveys 36(1981), no. 2, pp. 11–92 (1982)

External Links:

ISSN 0042-1316, Document, MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§21.1, §21.6(ii), §21.7(i), Figure 21.9.2, Figure 21.9.2, §21.9, §21.9, Sidebar 21.SB2, Ch.21, Notations T.

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Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions. Stud. Appl. Math. 107 (3), pp. 293–323.

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External Links:

ISSN 0022-2526, Document, MathReview, ZentralBlatt

Referenced by:

§10.20(ii), §2.8(i).

Encodings:

BibTeX

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Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point. Anal. Appl. (Singap.) 12 (4), pp. 385–402.

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External Links:

ISSN 0219-5305, Document, Link, MathReview (Thomas Mbah Acho), ZentralBlatt

Referenced by:

5th item, §14.32.

Encodings:

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18: 36.14 Other Physical Applications

… ►Diffraction catastrophes describe the (linear) wave amplitudes that smooth the geometrical caustic singularities and decorate them with interference patterns. …

19: William P. Reinhardt

… ►He has recently carried out research on non-linear dynamics of Bose–Einstein condensates that served to motivate his interest in elliptic functions. …

20: About Color Map

… ►The following figure illustrates the piece-wise linear mapping of the height to each of the color components red, green and blue, written as $⟨R,G,B⟩$. … ►We therefore use a piecewise linear mapping as illustrated below, that takes phase $0$ to red, $\pi /2$ to yellow, $\pi$ to cyan and $3\pi /2$ to blue. …