Given r(t)=ti+2sintj+2costk and u(t)=1/ti+2sintj+2costk, find
the following: 1. r(t) x u(t) 2. d/dt (r(t) x u(t)...
Given r(t)=ti+2sintj+2costk and u(t)=1/ti+2sintj+2costk, find
the following: 1. r(t) x u(t) 2. d/dt (r(t) x u(t) 3.now use
product rule for derivative of cross product of two vectors and
show same result
Given the vector function r(t)=〈√t , 1/(t-1) ,e^2t 〉 a) Find: ∫
r(t)dt b) Calculate the definite integral of r(t) for 2 ≤ t ≤ 3
can you please provide a Matlab code?
1. Let U = {r, s, t,
u, v, w, x, y,
z}, D = {s, t, u,
v, w}, E = {v, w,
x}, and F = {t, u}. Use roster
notation to list the elements of D ∩ E.
a.
{v, w}
b.
{r, s, t, u, v,
w, x, y, z}
c.
{s, t, u}
d.
{s, t, u, v, w,
x, y, z}
2. Let U = {r, s,
t, u, v, w, x,
y, z},...
Given following ODE's
1) x' = x / 1+t, with x(0) = 1 find x(2)
2) x' = t+x with x(0) = 1, find x(2)
3) x' = t-x, with x(1) =2 find x(3)
4) x' = t-x/t+x, with x(2) = 1, find x(4)
a) Solve each of the ODE's using Euler's method with h = 0.5,
and calculate the relative error
i) x' = x/1+t: Approximation ____________________ Relative
error: ________________
ii) x'= t+x; Approximation ____________________ Relative error:
________________
iii)...
Consider the 1D wave equation d^2u/dt^2 = c^2( d^2u/dx^2) with
the following boundary conditions: u(0, t) = ux (L, t) = 0 . (a)
Use separation of variables technique to calculate the eigenvalues,
eigenfunctions and general solution. (b) Now, assume L = π and c =
1. With initial conditions u(x, 0) = 0 and ut(x, 0) = 1, calculate
the solution for u(x, t). (c) With initial conditions u(x, 0) =
sin(x/2) and ut(x, 0) = 2 sin(x/2) −...
1. Consider the following second-order differential equation.
d^2x/dt^2 + 3 dx/dt + 2x − x^2 = 0 (a) Convert the equation into a
first-order system in terms of x and v, where v = dx/dt. (b) Find
all of the equilibrium points of the first-order system. (c) Make
an accurate sketch of the direction field of the first-order
system. (d) Make an accurate sketch of the phase portrait of the
first-order system. (e) Briefly describe the behavior of the
first-order...
Let T : P3(R) → P4(R) be defined by T(f(x)) = 5f′(x)-∫ f(t)dt
(integral from 0 to x)
1. Show that T is a linear transformation.
2.Find dim (P3(R)) and dim (P4(R)).
3.Find rank(T). Find nullity(T)
4. Is T one-to-one? Is T onto? Justify your answers.
. Given the
following non-periodic signal:
x(t) = 3 e-5t cos(12t)
u(t)
Find the Fourier transform expression X(ω) without
using Table.
Calculate the magnitude spectrum of X(ω) for ω = π/8, π/4, and
π/2