Assign R or S
RO "B" "C" "A" O RO t-Bu. CH3 hv HOS N- t-Bu Ts cat. HO• t-Bu N-Ts RO SO HO N-TS RO SO RO SO
i(z, t) i(z + Az, t) R'Δz 2 L'Az 2 v(2,t) G'Az C'Az v(z+Az, t) R'Az 2 L'AZ 2 Az dvíz, t) R'i(2,4) + 2 (a) Hint: Set up your equations using the appropriate KVL and/or KCL relationships for this circuit model of a transmission line differential section. Derive the following Partial Differential Telegraphy Equations; ai(z,t) (2.14 in Ulaby) az at ai(z,t) av(z,t) G'v(z,t) + C' (2.16 in Ulaby) дz at Sketch the lossless version of the equivalent circuit of...
Use Eq. (12) to find Z(f) when z(t) = Ate-' for t 2 0 and z(t) = 0 for t<0. lug talons 1966) * - 24 F (121 ionshin for n - 11
solve using Taylor series
Prove that if COS Z t /2, when z z2 (T/2)2 f(2) when z /2, then f is an entire function
5. Consider the nonlinear two dimensional Lotka-Volterra (predator-prey) system z'(t) = z(t)[2-2(t)-2y(t)l, y'(t) = y(t)12-y(t)--2(t)] (a) Find all critical points of this system, and at each determine whether or not the system is locally stable or unstable. (b) We proved in class, using the Bendixson-Dulac theorem, that this system has no periodic solution with trajectory in the first quadrant of the plane. Assuming this, use the Poincare-Bendixson theorem to prove that all trajectories (z(t),y(t)) of the system (2) with initial...
5. Consider the nonlinear two dimensional Lotka-Volterra (predator-prey) system z'(t) = z(t)[2-2(t)-2y(t)l, y'(t) = y(t)12-y(t)--2(t)] (a) Find all critical points of this system, and at each determine whether or not the system is locally stable or unstable. (b) We proved in class, using the Bendixson-Dulac theorem, that this system has no periodic solution with trajectory in the first quadrant of the plane. Assuming this, use the Poincare-Bendixson theorem to prove that all trajectories (z(t),y(t)) of the system (2) with initial...
Let T be a linear map from R3[z] to R2[z] defined as (T p)(z) =
p'(z). Find the matrix of T in the basis:
4 points] Let T be a linear map from Rals] to R12] defined as (TP)(z) = p,(z). Find the matrix of T in the basis: in R2[-]; ~ _ s, r2(z) (z-s)2 in R2 [2], where t and 8 are real numbers. T1(2 Find coordinates of Tp in the basis lo, 1, 12 (if p is...
1. Second order transients Z. Z V (t) Z Z N 2 The switch is in the left position and moves to the right position at t=r where >0. Let Z, be a resistor, R. Z be a inductor, Ly, 2, be a capacitor, Cr, Z. be a resistor, Rp. 2 be a resistor, Rs. Zo be a capacitor, Co, and the input voltage, vy(t) =uſt) volts. This question is about the voltage across the capacitor: Cg. viz., V.(s), v)....
Find the Peano range of the
Cauchy problem.
Z=38
{r' = (2 = (Z -t)y,-3<t< 3; y(1) = 2
The quantities 2,y,z and t satisfy z= f (2,y), 1 = g(t) et y=h(t). Given g(3) = -2 gl (3) = 3 h (3) = -2 hi (3) = -1, fic (-2,-2) = 3 fly (-2,-2) = 2 dz compute at t = 3 dt