Matlab Project 3 Spring 2014 Tim Pilachowski’s sections The due date is Monday April 28, 2014. (Yes – the date has been pushed up a little.) Turn in a printout of your published m-file. See Justin’s guide for instructions on how to write an mfile and how to publish it. Put the command lines for each question in the m-file separated by a blank line then a %% line and then another blank line. Each question should start with a clear all line followed by the declaration of any symbolic variables necessary for that problem. In other words each question should be completely self-contained. All 3D graphs should have view ([10 10 10]) set. 1. Plot the portion of x 2 + z 2 = 9 above the xy-plane and between y = − 1 and y = 2. 2. Plot the portion of the cone z = 9 − x 2 + y 2 inside the cylinder r = 2. r r r 3. Plot the vector field F ( x, y ) = 0.2 x 2 + y 2 i + 0.2 ( x − y ) j using meshgrid(-5:1:5,5:1:5). ( ) 4. A piece of wire is in the shape of the circle x 2 + y 2 = 1 . The density at any point is given by δ ( x, y ) = x 2 + y 4 . Find the mass of the wire. side information, not needed to answer the question: δ ( x, y ) could be in grams per cm in which case the mass would be grams. 5. Evaluate the line integral ∫ x + y ds where C is the straight line segment from (0, 1, 1) to (3, 2, 2). C 6. Evaluate the line integral ∫ yz dx + yz dy + y dz where C is the top half of y 2 + z 2 = 4 in the C yz-plane traveling from left to right. 7. Suppose Σ is the portion of the plane z = 10 − x − y inside the cylinder x 2 + y 2 = 1 . The surface Σ is submerged in an electric field such that at any point the electric charge density is δ ( x, y, z ) = x 2 + y 2 . Find the total amount of electric charge on the surface. side information, not needed to answer the question: δ ( x, y, z ) δ(x, y, z) could be in coulombs per cubic centimeter in which case the total charge would be in coulombs. r r r r 8. A fluid is flowing through space following the vector field F (x, y ) = y i − x j + z k . A filter is in the shape of the portion of the paraboloid z = x 2 + y 2 with 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3, oriented inwards (and upwards). Find the rate at which the fluid is moving through the filter. r side information, not needed to answer the question: The fluid flow F could have units g/(cm2s) in which case the total flow would be in grams per second. Math 241, T Pilachowski, Spring 2014

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