374chw4 - HW#4 —Phys374—Spring 2008 Prof. Ted Jacobson...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

This note was uploaded on 12/29/2011 for the course PHYSICS 374 taught by Professor Jacobson during the Fall '10 term at Maryland.

Page1 / 2

374chw4 - HW#4 —Phys374—Spring 2008 Prof. Ted Jacobson...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online