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transformation. Perform the mappings of lines x- 2 and y 3 under the transformation w = z2 where z = x + iy. Compute the angles between the curves in the u-v plane at the points of intersection. Henc...
As we discussed in class, contormal mapping preserves angles under transformation. Perform the mappings of lines...
As we discussed in class, contormal mapping preserves angles under transformation. Perform the mappings of lines x 2 and y 3 under the transformation w z2 where z-x y. Compute the angles between the curves in the u-v plane at the points of intersection. Hence check if the angles between the lines in the z-plane are the same as the angles between the curves in the u-v plane.
Complex affine transformation in plane s w = az+β, where:= x+iy, w = x, + iy'. For complex numbers α = αι + ia2, β = β1 + 2β2 rewrite this transformation as affine transformation in plane bet...
Complex affine transformation in plane s w = az+β, where:= x+iy, w = x, + iy'. For complex numbers α = αι + ia2, β = β1 + 2β2 rewrite this transformation as affine transformation in plane between coordi nates (x, y) and (x', y/). Identify corresponding linear 2x2 transforma- tion matrix A and translation vector t. Show that matrix representa- tion of this affine transformation is
Complex affine transformation in plane s w = az+β, where:= x+iy, w =...
z+1 The linear fractional transformation shown below is related to w = u + jv and...
z+1 The linear fractional transformation shown below is related to w = u + jv and z = x + jy w= z-2' a. Calculate the curves that the lines v = constant maps to in the x-y plane, b. Calculate the curves that the lines y = constant maps to in the u-v plane, c. What is the line in the x-y plane that maps to a line in the u-v plane?
(z2 + y*) dV where D is the region inside the cone z- V z2 +アbelow the plane z = 3, and inside the first ai 1- octant z 2 0,y 2 0,z2 0 (z2 + y*) dV where D is the region inside the cone z- V z2...
(z2 + y*) dV where D is the region inside the cone z- V z2 +アbelow the plane z = 3, and inside the first ai 1- octant z 2 0,y 2 0,z2 0
(z2 + y*) dV where D is the region inside the cone z- V z2 +アbelow the plane z = 3, and inside the first ai 1- octant z 2 0,y 2 0,z2 0
(Complex analysis) Exercise 5. Find the images of the following curves under the linear mapping w = (i + V3)2 + iV3-1, where z = x + iy: a)y=0 b) x = 0 c) 2 y1 d) x2 + y2 + 2y 1 Answer b) v3u c) (11...
(Complex analysis)
Exercise 5. Find the images of the following curves under the linear mapping w = (i + V3)2 + iV3-1, where z = x + iy: a)y=0 b) x = 0 c) 2 y1 d) x2 + y2 + 2y 1 Answer b) v3u c) (11 + 1)2 + (v-V3)2 = 4 d) 11 2 + U2-8
Exercise 5. Find the images of the following curves under the linear mapping w = (i + V3)2 + iV3-1, where...
410. [V] The transformation T.1.1: R3 R3, Tk,1,1 (u, v, w) = (x, y, z) of...
410. [V] The transformation T.1.1: R3 R3, Tk,1,1 (u, v, w) = (x, y, z) of the form x = ku, y = 0, z = w, wherek #1 is a positive real number, is called a stretch if k > 1 and a compression if 0 <k < 1 in the x-direction. Use a CAS to evaluate the integral e-(4x2+9y?+252) dx dy dz on the solid S = {(x, y, z)|4x² +9y2 + 25z< 1} by considering the compression...
let u= ln(x) and v=ln(y) w=ln(z) where x,y,z>0 .Write thr following wxpressiins in terms of u,v,...
let u= ln(x) and v=ln(y) w=ln(z) where x,y,z>0 .Write thr following wxpressiins in terms of u,v, and w. a) ln( squareroot x^5)/ y^3z^2) B) ln (squareroot x^3 4squaroot y)
QUESTION 2 ONLY Question 1:(1 point) Consider the curves y = 7z2 +4x and y =-z2 + 4 a) Determine their points of interse...
QUESTION 2 ONLY
Question 1:(1 point) Consider the curves y = 7z2 +4x and y =-z2 + 4 a) Determine their points of intersection (x^,y1) and (x2,2),ordering them such that xi < x2 What are the exact coordinates of these points? ,y1= b) Find the area of the region enclosed by these two curves. t0.001 Give its approximate value within Answer: Question 2: (1 point) Let S be the solid with flat base, whose base is the region in the...
)Given a 4-node element in x-y plane as shown here: Node X 3 3 1 8 a) Using the shape functions in u-v plane, determine an expression for mapped points from u-v to x-y, i.e. x- x(u, v) and y -y(u...
)Given a 4-node element in x-y plane as shown here: Node X 3 3 1 8 a) Using the shape functions in u-v plane, determine an expression for mapped points from u-v to x-y, i.e. x- x(u, v) and y -y(u, v), for points within the 4-node element in u-v plane. Then, determine value of x and y for a point with (u, v)-(0.3,0.3). (10 points) b) Determine the value of Jacobian matrix, [J], and its determinant for such mapping...
You are given the following multivariate PDF (x, y, z) ES fxx.2(x, y, z) =- 0 else where S-((z, y...
You are given the following multivariate PDF (x, y, z) ES fxx.2(x, y, z) =- 0 else where S-((z, y, z) 1x2 + уг + z2 < 1} (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S....
As we discussed in class, contormal mapping preserves angles under transformation. Perform the mappings of lines x 2 and y 3 under the transformation w z2 where z-x y. Compute the angles between the curves in the u-v plane at the points of intersection. Hence check if the angles between the lines in the z-plane are the same as the angles between the curves in the u-v plane.
Complex affine transformation in plane s w = az+β, where:= x+iy, w = x, + iy'. For complex numbers α = αι + ia2, β = β1 + 2β2 rewrite this transformation as affine transformation in plane between coordi nates (x, y) and (x', y/). Identify corresponding linear 2x2 transforma- tion matrix A and translation vector t. Show that matrix representa- tion of this affine transformation is
Complex affine transformation in plane s w = az+β, where:= x+iy, w =...
z+1 The linear fractional transformation shown below is related to w = u + jv and z = x + jy w= z-2' a. Calculate the curves that the lines v = constant maps to in the x-y plane, b. Calculate the curves that the lines y = constant maps to in the u-v plane, c. What is the line in the x-y plane that maps to a line in the u-v plane?
(z2 + y*) dV where D is the region inside the cone z- V z2 +アbelow the plane z = 3, and inside the first ai 1- octant z 2 0,y 2 0,z2 0
(z2 + y*) dV where D is the region inside the cone z- V z2 +アbelow the plane z = 3, and inside the first ai 1- octant z 2 0,y 2 0,z2 0
(Complex analysis)
Exercise 5. Find the images of the following curves under the linear mapping w = (i + V3)2 + iV3-1, where z = x + iy: a)y=0 b) x = 0 c) 2 y1 d) x2 + y2 + 2y 1 Answer b) v3u c) (11 + 1)2 + (v-V3)2 = 4 d) 11 2 + U2-8
Exercise 5. Find the images of the following curves under the linear mapping w = (i + V3)2 + iV3-1, where...
410. [V] The transformation T.1.1: R3 R3, Tk,1,1 (u, v, w) = (x, y, z) of the form x = ku, y = 0, z = w, wherek #1 is a positive real number, is called a stretch if k > 1 and a compression if 0 <k < 1 in the x-direction. Use a CAS to evaluate the integral e-(4x2+9y?+252) dx dy dz on the solid S = {(x, y, z)|4x² +9y2 + 25z< 1} by considering the compression...
QUESTION 2 ONLY
Question 1:(1 point) Consider the curves y = 7z2 +4x and y =-z2 + 4 a) Determine their points of intersection (x^,y1) and (x2,2),ordering them such that xi < x2 What are the exact coordinates of these points? ,y1= b) Find the area of the region enclosed by these two curves. t0.001 Give its approximate value within Answer: Question 2: (1 point) Let S be the solid with flat base, whose base is the region in the...
)Given a 4-node element in x-y plane as shown here: Node X 3 3 1 8 a) Using the shape functions in u-v plane, determine an expression for mapped points from u-v to x-y, i.e. x- x(u, v) and y -y(u, v), for points within the 4-node element in u-v plane. Then, determine value of x and y for a point with (u, v)-(0.3,0.3). (10 points) b) Determine the value of Jacobian matrix, [J], and its determinant for such mapping...
You are given the following multivariate PDF (x, y, z) ES fxx.2(x, y, z) =- 0 else where S-((z, y, z) 1x2 + уг + z2 < 1} (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S....
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