Microsoft PowerPoint - 高等应用数学Ch1.pdf

Part A An Overview of the Interaction of Mathematics and Natural Science 5 Ch 1 1 1 1 2 1 3 6 1 1 7 8 9 10 19 Sir Isaac Newton 11 12 20 40 50 13 John von Neumann J F 1994 14 Von Karman Theodore von Karman Ludwig Prandtl Felix Klein 15 Bai 16 20 80 17 1 0 Tf m l g 0 f t m l g m l g 1 2 l g 1 2 0 1 1 1 Tl gf 1 2 0 Tl gF m 18 2 0 n n tt a 1nn tat a a a 1 1 2 nn t t 2 1nnn tatbt 19 2 1 1 nnn xfxx nn tcxd 11nn tcxd 2 42 a aa cd bb 2 4 a a bc 20 2 1yx 0 2 1 1 n x 21 1 2 p 3 22 2 3 23 Fourier Fourier idea case study formulation solution interpretation 24 25 1 2 1 2 3 26 1 27 1010 1010 109 1010 28 29 30 31 Maxwell 32 10 12 Jm 3 130 10 5 0 4 0 1 0 07 0 05 33 x0 m kxxm x u x 34 x y z u v w x y z u v w t t x x x y y y z z z u u u v v v w w w x y z u v w t dxdydzdudvdw 35 dudvdwtwvuzyxmtzyx 2 0 2 0 2 0 000000 zzyyxx dzdydxtzyx GtzyxV 36 m1 m2 12 2 m m FG r 1 m VG r 1 2 mdV aG drr r m1m2 0 r F 37 z V dt dw y V dt dv x V dt du w dt dz v dt dy u dt dx 0 wz V vy V ux V z w y v x u t 38 1111 2222 xx uu ttxx uu tx u t u x du dtu u x xx x 1 2 uu u u u 1 2 uu du dt du dt 111 222 11 22 x uu txx uu tuuu t du xx u txx uu tx t dt 0 dud u txdtudt x u t 39 t x y z u v w t x y z t V x y z t x y z u v w t t t t x y z u v w t t 0 VVV uvw txyzxuyvzw 40 Stationary z w 0 V w zzw zmz w dw VV z 41 0 V w zzw dw w dz z d dzdw V w z 1 0 V ddz zwzw 42 dzdw V w z 0 V wdwdz z 2 1 2 wV zE const 2 1 2 fwV z 43 Gauss 2 1 2 00 wV z E A eA e 0 V z ze 2 1 2 00 0 2 wV z V zV z zmA edwA mee 0 V z 0 44 Poisson 2 0 2 0 2 0 000000 zzyyxx dzdydxtzyx GtzyxV 2 4VG 2 2 4 d V Gz dz 222 2 222 xyz 45 2 1 2 0 wV z w zA e 0 V z ze 2 2 4 d V Gz dz 22 22 0 1 ln d Vdz dzdz 46 1 2 3 4 5 6 Gauss 47 B Lindblad 48 1 3 49 50 51 cAMP 3 5 Cyclic 3 5 adenosine monophosphate 52 a density of amebae density of attractant J Ja flux density Q Qa net rate of creation 53 x x x xxxx xx a x t dxJ x tJ xx tQ x t dx t 0 J x t J x x t xx x 1Q a x tJ x t Q x t tx 54 r a x t Jx tF x r a x t Jx t x motility c Jx ta x strength of chemotaxis 55 a x tJ x t tx rc JJJ aa a txxx 10 56 a a J Q tx a JD x D diffusivity a Qfak 2 2 fakD tx f rate of secretion k rate of decay 11 57 00 fak 00 aa aa a txxx 2 2 fakD tx 58 a 0 atxaatx 0 x tx t 10 aa a txxx 22 0 22 aaa aa txxxx 59 22 0 22 aa a txx 11 2 2 fakD tx 17 16 60 22 0 22 aa a txx 2 2 fakD tx 1sin t aCqxe 2sin t Cqxe 22 102 2 12 0 0 q Ca q C fCkDq