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Unformatted text preview: HW#4 —Phys374—Spring 2008 Prof. Ted Jacobson Due before class, Friday, Feb. 29, 2008 Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/374c/ [email protected] 1. Problems 5.2a,b. ( Pressure gradient ) (For 5.2a, scan, photocopy, or trace the map.) For 5.2b, you’ll have to work out or look up the distance across Ireland in the relevant direction.) [5+5=10 pts.] 2. Consider the function f ( x, y, z ) = ax 2 + by 2 + cz 2 . [2+2+2+2+2=10 pts.] (a) Find ∇ f . (b) Find the rate of change of f at the point (1 , 1 , 1) in the direction of the position vector r . ( Caution : r is not a unit vector.) (c) Find the rate of change of f at the point (1 , 1 , 1) in the direction of most rapid increase of f . (d) The level sets f = const . are ellipsoids. Find the unit normal to the ellipsoid at the point (1 , 1 , 1). (e) What is the angle between r and the normal to the ellipsoid at (1 , 1 , 1)? Check that in the spherically symmetric case a = b = c the angle is zero....
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This note was uploaded on 12/29/2011 for the course PHYSICS 374 taught by Professor Jacobson during the Fall '10 term at Maryland.
- Fall '10