In of Exercises 14.3 you were asked to find the time-dependent temperatures u(r, t) within a unit sphere. The temperatures outside the sphere are described by the boundaryvalue problem 02 u 0r 2 2 r 0u 0r 0u 0t , r 1, t 0 u(1, t) 100, t 0 limrSq u(r, t) 0 u(r, 0) 0, r 1. Use the Laplace transform to find u(r, t). [Hint: After transforming the PDE, let v(r, s) r U(r, s), where +{u(r, t)} U(r, s).]

Quadric Surfaces SUGGESTED REFERENCE MATERIAL: As you work through the problems listed below, you should reference Chapter 11.7 of the rec- ommended textbook (or the equivalent chapter in your alternative textbook/online resource) and your lecture notes. EXPECTED SKILLS: ▯ Be able to compute & traces of quadic surfaces; in particular,...