Advanced Engineering Math II phần 4 pot

... of this. (B) Potential between two non-coaxial cylinders. Find the potential between two cylinders C 1 : |z| = 1 being grounded (potential 0) and C 2 : |z - 0 .4| = 0 .4 having a potential of 110 ... the potential, complex potential, equipotential lines, and lines of force of between two parallel plates at x = -5 and x = 10 having potentials 200 and 500 volts respectively. 2. Find the potent...

Ngày tải lên: 08/08/2014, 11:21

... C- R are called conjugate harmonic functions. Advanced Engineering Math II Math 144 Lecture Notes by Stefan Waner (First printing: 2003) Department of Mathematics, Hofstra University 7 Definition ... Representation of Addition- in class. (Multiplication later) Examples 1.3 (a) 3 +4 = (3, 0)+ (4, 0) = (7, 0) = 7 (b) 3 4 = (3, 0) (4, 0) = (12-0, 0) = (12, 0) = 12 (c) (0, y) = y(0,...

Ngày tải lên: 08/08/2014, 11:21

... πi/2; (e) ln(-1) = πi + 2nπi; Ln (-1) = πi; (f) ln(3-4i) = ln5 + i arg(3-4i) + 2nπi = ln5 + i arctan (4/ 3) + 2nπi; Ln(3-4i) = ln5 + i arctan (4/ 3). More Properties 1. ln(z w) = lnz + lnw; ln(z/w) ... arg(z) ≠ π} Æ CI 4. ln 0 is still undefined, as there is no complex number w such that e w = 0. Examples 3.7 (a) ln1 = 0 + 2nπi = 2nπi; Ln 1 = 0; (b) ln4 = 1.386 + 2nπi; Ln 4 = 1.386 (c...

Ngày tải lên: 08/08/2014, 11:21

... associated conjugate potential §(z) = A Arg(z) For a circular symmetry situation (potential independent of ø), the complex potential F(z)= ALn(z) + B is just a linear function of Ln(z). (C) Potential in ... 0 (since the potential is 0 at infinity. Also, the potential is undefined at the origin, since the potential is infinite on the actual wire. We can obtain A by measuring at the potential c...

Ngày tải lên: 08/08/2014, 11:21

... = 0.05+0.37*(t^2+k^2+2*((t^2-k^2- 4) ^2 +4* t^2*k^2)^.5/2)+0.12166*(t+2*k)+(((t^2-k^2- 4) ^2 +4* t^2*k^2)^.5/2+(t^2-k^2- 4) /2)^.5*(0. 74* t+0.12166)+(((t^2-k^2 -4) ^2 +4* t^2*k^2)^.5/2- (t^2-k^2 -4) /2)^.5 *(.37*k+0. 243 32) 46 1 2 4 –1 (a) Find a mapping from the ... ((t^2-k^2 -4) ^2 +4* t^2*k^2)^.5/2 S = (t^2-k^2 -4) /2 R+S = (((t^2-k^2 -4) ^2 +4* t^2*k^2)^.5/2+(t^2-k^2 -4) /2)^.5...

Ngày tải lên: 08/08/2014, 11:21

... the potential, complex potential, equipotential lines, and lines of force of between two parallel plates at x = -5 and x = 10 having potentials 200 and 500 volts respectively. 2. Find the potential, ... Representation of Addition- in class. (Multiplication later) Examples 1.3 (a) 3 +4 = (3, 0)+ (4, 0) = (7, 0) = 7 (b) 3 4 = (3, 0) (4, 0) = (12-0, 0) = (12, 0) = 12 (c) (0, y) = y(0, 1) = yi...

Ngày tải lên: 27/06/2014, 14:20

...

Ngày tải lên: 05/08/2014, 14:21

... (0.83 14 × 298/0.79) = 6190–298 × 193.5 + 100 × 31 .4 = 48 ,333 kJ kmole –1 . Therefore, φ ∞ = 0.6 × ( 46 981) + 0 .4 × ( 48 333) = 47 521.8 kJ kmole –1 , and w ch = –5 247 3.8 – ( 47 521.8) = 49 52 ... = 48 5.8 kJ kg –1 . Therefore, ˙ W cv,opt = 10 43 0.2 + 0.89×28.6 – (10×335.3 + 0.89 48 5.8) = 544 kW, and I= ˙ W cv,opt – ˙ W = 544 – 0 = 544 kW. Remarks Hot combustion products en...

Ngày tải lên: 08/08/2014, 15:21

... this: S# DURING S1 [d 04, d10 ] S1 [d05, d10 ] S1 [d09, d10 ] S1 [d06, d10 ] S2 [d02, d 04] S2 [d03, d03] S2 [d08, d10 ] S2 [d09, d10 ] S3 [d08, d10 ] S4 [d06, d10 ] S4 [d 04, d08 ] S4 [d05, d10 ] Temporal ... to ponder over: • What happens to the interval [now, d 14 ] at midnight on day 14? • What is the value of END([d 04, now]) on day 14? Is it d 14 or is it now? We believe it is hard...

Ngày tải lên: 08/08/2014, 18:21