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question a rectangular channel of width w and depth h meters lies in thej direction at a point d1 meters from one side
question 1 use the change of coordinates x 2s t y s - t to compute the integral rxy da where r is the parallelogram
question two independent random numbers x and y from a normal distribution with mean 0 and standard deviation sigma
question a river follows the path y fx where x y are in kilometers near the sea it widens into a lagoon then narrows
question 1 a change of coordinates x xs t y ys t where the rectangle 0 le s le 1 0 le t le 1 in the st-plane
question suppose you are standing at a point on the equator of a sphere parameterized by spherical coordinates theta0
question a decorative oak post is 48 long and is turned on a lathe so that its profile is sinusoidal as shown in
question 1 describe in words the curve phi pi4 on the surface of the globe2 describe in words the curve theta pi4 on
question you are at a point on the earth with longitude 80deg west of greenwich england and latitude 40 north of the
question 1 draw two vector fields that have positive divergence everywhere2 draw two vector fields that have negative
qusetion 1 use the geometric definition of divergence to find div vrarr at the origin where vrarr -rrarr check that
question for any positive number a the problem of calculating the square rootnbspradica is often done by applying
question a smooth vector field grarr has curl grarr 0 0 0 2irarr - 3jrarr 5krarr estimate the circulation around a
question a large fire becomes a fire-storm when the nearby air acquires a circulatory motion the associated updraft has
question a vortex that rotates at constant angular velocity omega about the z-axis has velocity vector field vrarr
question a a river flows across the xy-plane in the positive x-direction and around a circular rock of radius 1
qusetion a fluid is flowing along a cylindrical pipe of radius a in the irarr direction the velocity of the fluid at a
question a basic property of the electric field erarr is that its divergence is zero at points where there is no charge
question a find the flux of the given vector field out of a cube in the first octant with edge length c one corner at
question the flux of the constant vector field a b c through the square of side 2 in the plane x 5 oriented in the
question find the flux of the vector field through the surface s1 frarr xirarr through a square of side 3 in the plane
question find the flux of the vector field through the surface s1 frarr yjrarr through the square of side 4 in the
question a find divrrarrrrarr2 where r xi yj for r 0b can you use the divergence theorem to compute the flux of
question suppose div frarr xyz2a find div frarr at the point 1 2 1 note you are given div frarr not frarrb using your