Sample problems 6.pdf - ECE 333 UMass Amherst Sample problems 6 1 Coordinate systems Given points with the Cartesian coordinates(\u22121,3,4 find(a

# Sample problems 6.pdf - ECE 333 UMass Amherst Sample...

• Homework Help
• 9

This preview shows page 1 - 9 out of 9 pages.

ECE 333 UMass Amherst Sample problems 6 1. Coordinate systems. Given points 𝐴𝐴 with the Cartesian coordinates 𝐴𝐴 : ( 1,3,4) , find: (a) Coordinates of 𝐴𝐴 in cylindrical and spherical coordinates. (b) Position vector of 𝐴𝐴 in cylindrical and spherical coordinates. (c) Base unit vectors of cylindrical coordinates at point 𝐴𝐴 in terms of base unit vectors of spherical coordinates at the same point.
ECE 333 UMass Amherst 2. Gradient. Consider scalar field 𝑓𝑓 = 4 𝑥𝑥 2 𝑦𝑦 − 𝑧𝑧 2 , (a) Find 𝛻𝛻𝑓𝑓 and its directional derivative at point 𝐴𝐴 (2,0, 1) along the direction 𝒅𝒅 = ( 𝒙𝒙 + 𝒛𝒛 )/ 2 . (b) Compute the line integral of 𝛻𝛻𝑓𝑓 along the straight line from origin to point 𝐴𝐴 and verify that it is equal to 𝑓𝑓 ( 𝐴𝐴 ) − 𝑓𝑓 ( 𝑂𝑂 ). (c) Compute the line integral of 𝛻𝛻𝑓𝑓 along the path defined by two straight lines: first from the origin to point 𝐵𝐵 = (2,0,0) and then from point 𝐵𝐵 to point

#### You've reached the end of your free preview.

Want to read all 9 pages?

• Fall '09

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern