{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

374bhw4 - ϕ in the direction of most rapid increase at the...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
HW#4 —Phys374—Spring 2007 Prof. Ted Jacobson Due before class, Friday, Feb. 23, 2007 Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/374b/ [email protected] 1. Problems 5.2a,b. ( Pressure gradient ) (For 5.2a, photocopy 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. Problems 5.2e,f,g. ( Pressure force ) Snieder basically does these for you, so all that’s left to do is just put in a few precise and concise words explaining why each equation is true. (Note ˆ x should not be present in (5.13) & (5.14) since teh left hand side is just a component of the force vector. [4+3+3=10 pts.] 3. Consider the function ϕ ( x, y, z ) = z - 3 xy . (a) Find ϕ . [3 pts.] (b) What is the rate of change of ϕ at the point (0 , 1 , 2) in the direction of the vector ˆ i + 2 ˆ j + 3 ˆ k ? ( Be careful , this is not a unit vector.) [4 pts.] (c) What is the rate of change of
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ϕ in the direction of most rapid increase at the point (0 , 1 , 2)? [3 pts.] 4. Derive the identity ∇ · ( f v ) = ∇ f · v + f ∇ · v , (1) where f is a scalar field and v is a vector field. [5 pts.] 5. Evaluate the expression ∇ · r , (2) where r is the position vector from the origin to the point r , using (i) Cartesian coordinates and (ii) spherical coordinates (cf. (6.32)). [3+2=5 pts.] 6. (a) Find the most general function f ( r ) of only the radial coordinate r = | r | such that ∇ · ( f r ) = 0 except possibly at the origin r = 0. (b) Find the most general function g ( r,θ,ϕ ) such that ∇ · ( g r ) = 0, again except possibly at the origin r = 0. [4+1=5 pts.] 7. Problems 10.1a,b,c,d. ( Curvature of a function ) [2+1+4+3=10 pts.] 8. Problem 10.1 g ( Stability of equilibrium ) [5 pts.]...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern