ANSWER:-
4.37. Compute the following integrals. (a) Sci-12 12adz exp(2) JC(0,2) Z(z -3) (a) exp(z) JC(0,4) Z(z...
Convolution Integrals. For part A the solution I got was
t*exp(z*t) and for part B the solution I got was (exp(z2*t) -
exp(z1*t))/(z2-z1). I need help with the third part of the question
calculating (f * f)(t) without computing any integrals.
f(t -s)g(s)ds by hand for (a) and (b) below Calculate (a) f(t) g(t) = et where z is a constant e21t and g(t) e22t where z1 and z2 are constants (b) f(t) Use your results from parts (a) and...
Exercise 12: Residues and real integrals (a) [6+4 points) Compute the residues for all isolated singularities of the following functions (i) f(2)== (2-) tan(2), (i) 9(2):= z2 sin () (b) (4+6+5 points) Compute (using the Residue theorem) (1) cos(72) ( d, A3 := {z € C:<3), 243 := {Z EC: | = 3}, 34, (2-1)(2 + 2)2(2-4) : 43 € C:21 <3}, po 12 To (x2 + 4)2 da, 24 2 + 4 cosat. J 5 + 4 sin(t)
Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0 < u 2, 0 £1 3
Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0
3. 20 marks] Compute these integrals, with γ a circle of radius 2, Centre at origin, oriented counterclockwise: 2 2z (z-1)3, 22 42 γ ~2 + 8.
1) (30 pts) Compute the following indefinite integrals: le 12 de
3-5.2. Let X, Y, and Z have the joint pdf 3/2 1 |ryz exp exp 27T 2 where -o<x < o,-00< y < oo, and 00< z < 00. While X, Y, and Z are obviously dependent, show that X, Y, and Z are pairwise independent and that each pair has a bivariate normal distribution
3-5.2. Let X, Y, and Z have the joint pdf 3/2 1 |ryz exp exp 27T 2 where -o
subject is differential equations
please hurry up
(5) (12 poins)(a) Compute the sine series for the function f such that f(z) r(4-z) on the interval l0,4 (b) Compute the solution u(z,t) for the partial differential equation with z in the interval (0,4) and t > 0: 3tit tigr with u(0,t) = u(4,t)-0 for t > 0 u(z, 0)(4-a) for 0 <4 (boundary conditions) (initial conditions)
(5) (12 poins)(a) Compute the sine series for the function f such that f(z) r(4-z)...
evaluate the following integrals. please show procedure.
Develop g(z)= 1/(z-1)(z-2) into a laurent series that is valid
for the following anular domains.
4) 23. 01/22 dz Y a) r=1121=5), bydle-il-24 Sol: Ti r = {12-21 = 2 3 4 Sol: Ti 1 5) S dz 23(2-1) 4 r 6) J ze² z ²-1 dz 8=2 Izl=2) Sol: 2li cash (1) Y 9) 0시레시 (o) 0 12-2[J.
get the value of the following integrals
where c is the circle (abs)z=3
2 dz e*"dz , donde C (z+, uientes: A) φ
3. Using the graph off compute the definite integrals (use known geometric formulas). 2 4 (n) (2) de (w) | sle)dr = S $12)de - [ Педаг . (e) 4. Using the graph of g compute the definite integrals. area 3 arca-6 6 7 5 area (b) (a) [*ola) dr = 9(x) dx = (c) (a)dx (d) (Circle one) ne) . 9(1) dr = positive / negative / zero 2