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Philosophical Magazine Volume 92, 2012 - Issue 32
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Commentary

Laplace and the era of differential equations

Peter Weinberger Center for Computational Nanoscience, Seilerstätte 10/22, A-1010 Vienna, AustriaCorrespondence[email protected]
Pages 3882-3890 | Received 07 Feb 2012, Accepted 22 May 2012, Published online: 26 Jun 2012

References

  • Le Baron Fourier , M . 1821 . Phil. Mag. Series 2 , 6 ( 35 ) : 370
  • Dickson , W . 1801 . Phil. Mag. Series 1 , 9 ( 33 ) : 39
  • Marat , Mr . 1810 . Phil. Mag. Series 1 , 36 ( 149 ) : 186
  • Englefield , HC . 1815 . Phil. Mag. Series 1 , 45 ( 201 ) : 15
  • The Laplace equation, is a second-order partial differential equation with f being a real-valued function. If where g is also a real-valued function, then the Laplace equation is called the Poisson equation
  • In Cartesian coordinates the Laplace equation is given by x, y and z being real variables
  • White , T . 1813 . Phil. Mag. Series 1 , 41 ( 177 ) : 8
  • In spherical coordinates the Laplace equation reads as
  • Thomson , J . 1813 . Phil. Mag. Series 1 , 41 ( 181 ) : 357
  • Gordon , J . 1831 . Phil. Mag. Series 2 , 9 ( 52 ) : 253
  • Phil. Mag. Series 1 29 (115) (1807) p.211
  • Ivory , J . 1826 . Phil. Mag. Series 1 , 68 ( 341 ) : 161
  • The Laplace probability density function is defined by where x is a random variable, b > 0 and α is a so-called “location parameter”, f(x; 0, 1) = exp(−x)/2
  • Count De Laplace, Phil. Mag. Series 1 58 (280) (1821) p.133
  • Challis , J . 1829 . Phil. Mag. Series 2 , 6 ( 32 ) : 123
  • Challis , J . 1833 . Phil. Mag. Series 3 , 3 ( 15 ) : 185
  • Challis , J . 1840 . Phil. Mag. Series 3 , 17 ( 112 ) : 462
  • Airy , GB . 1840 . Phil. Mag. Series 3 , 17 ( 113 ) : 481
  • Challis , J . 1841 . Phil. Mag. Series 3 , 18 ( 115 ) : 130
  • Airy , GB . 1841 . Phil. Mag. Series 3 , 18 ( 118 ) : 321
  • Challis , J . 1841 . Phil. Mag. Series 3 , 19 ( 121 ) : 63
  • Airy , GB . 1841 . Phil. Mag. Series 3 , 19 ( 122 ) : 143
  • Challis , J . 1841 . Phil. Mag. Series 3 , 18 ( 119 ) : 477
  • Challis , J . 1842 . Phil. Mag. Series 3 , 20 ( 129 ) : 84
  • Challis , J . 1842 . Phil. Mag. Series 3 , 20 ( 131 ) : 281
  • Challis , J . 1842 . Phil. Mag. Series 3 , 21 ( 136 ) : 101
  • Stokes , GG . 1842 . Phil. Mag. Series 3 , 21 ( 138 ) : 297
  • Challis , J . 1842 . Phil. Mag. Series 3 , 21 ( 140 ) : 423
  • Stokes , GG . 1843 . Phil. Mag. Series 3 , 22 ( 142 ) : 55
  • Schrödinger , E . 1926 . Ann. Phys. , 79 : 361
  • Schrödinger , E . 1926 . Ann. Phys. , 79 : 489
  • Schrödinger , E . 1926 . Ann. Phys. , 80 : 437
  • Schrödinger , E . 1926 . Ann. Phys. , 81 : 109
  • A Laplace transformation is defined by where f(t) is a function locally integrable on [0, ∞). In short: a Laplace transformation converts a function f(t) with a real argument t into a function F(s) with a complex argument s
  • Hilbert , D and Courant , R . 1991 . “ Methoden der mathematischen Physik ” . In Methods of Mathematical Physics , New York : John Wiley . first published in 1924; present English edition

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