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Vector Calculus
Find velocity,acceleration,speed,T,B,N,k and equations for the osculating, normal, and rectifying planes for the curve r(t)=(cost)i+(sint)j-k at t=0.
Vector Calculus
Find the curl of the vector field A=ω ρ e^-( ρ/α )^2 uΦ ,where α and ω are constant . Both analytically and by use of the curl function .
Vector Calculus
Find the angles which the vector 3i-6j+3k makes with the coordinate axes.
Vector Calculus
Verify Stoke’s theorem for the vector
[b]A[/b]=(2x-y)[b]i[/b]-yz[sup]2[/sup][b]j[/b]-y[sup]2[/sup]z[b]k[/b],
& where S is the upper half surface of the sphere x[sup]2[/sup] + y[sup]2[/sup] + z[sup]2[/sup] = 1 and C is its boundary
[b]A[/b]=(2x-y)[b]i[/b]-yz[sup]2[/sup][b]j[/b]-y[sup]2[/sup]z[b]k[/b],
& where S is the upper half surface of the sphere x[sup]2[/sup] + y[sup]2[/sup] + z[sup]2[/sup] = 1 and C is its boundary
Vector Calculus
Given the coordinate transformation
u[sub]1[/sub] = xy
2u[sub]2[/sub] = x[sup]2[/sup] + y[sup]2[/sup]
u[sub]3[/sub] = z,
Determine if the coordinate system is orthogonal.
u[sub]1[/sub] = xy
2u[sub]2[/sub] = x[sup]2[/sup] + y[sup]2[/sup]
u[sub]3[/sub] = z,
Determine if the coordinate system is orthogonal.
Vector Calculus
Determine if the following vector is solenoidal,
A = 3y^4 z^2 i + 4x^3 z^2j- 3x^2y^2
A = 3y^4 z^2 i + 4x^3 z^2j- 3x^2y^2
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