please show all steps Find L{f}(s) directly by evaluating the integral if 2t when 0 <t<3,...
Q2: Find the complex Fourier series (show your steps) - T < x <07 f(x) 0 < x < Q1: Find the Fourier transform for (show your steps) - 1<x< 0 Otherwise (хе f(x) = { 0,
1. (5 points) Let 0 <t<4 f(t) = {t, t24 Find L{f(t)} if it exists. For what values s does the Laplace transform exist?
#6.) Given f(t)=-2:+8, Ost<4, f(t+4)= f(t). Find F(s)=L{f(t)} of the Periodic Function.
Show Sketch and all steps. Problem 18 Use the Divergence Theorem to calculate the surface integral || FdS , F(x,y,z) =< x²yz,xy-z, xyz? > S is the surface of the box enclosed by the planes x = 0, x = a, y = 0, y = b, z = 0, and z = C, where a, b, c are positive numbers.
please follow instructions exactly and explain all steps and variables 3. (9 pts) Consider the function: (1-t, t < 4, f(t) = { 12 - 16, 24. a. Represent f(t) using a combination of Heaviside step functions, h(t -c). b. Find the Laplace transform F(s) = L{f(t)}. Do not use the integral definition of the Laplace transform.
Find the Laplace Transform (d) f(t) = te, 0<t<1, et, t > 1. l
2t +1 if 0 <t< 2 Consider f(t) = { | 3t if t > 2. (a) Use the table of Laplace transforms directly to find the Laplace transform of f. (b) Express f in terms of the unit step function, then use Theorem 6.3.1 to find the Laplace transform of f.
Find the Laplace transform of the given function Solve the integral equation f(t) = { 0 < t < 2 t 22 t y(t) = 4t – 3 y(z)sin(t – z)dz 0
10 sin 2t if 0 <t< 4. (a) Let r(t) if t > T Show that the Laplace transform of r(t) is L(r) 20(1 - e - e-78) 32 + 4 (b) Find the inverse Laplace transform of each of the following functions: s – 3 S2 + 2s + 2 20 ii. (52 + 4)(52 + 25 + 2) 20e-S ini. (s2 + 4)(52 + 25 + 2) (c) Solve the following initial value problem for a damped mass-spring...
Integral Transform Find the Laplace transform for the periodic function f(t) = f(t+2) and f(t) = t for 0 <t< 2.