This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: M 427L Second Exam Put your answers to all the questions on the scantron sheet. Be sure you put your eid on the scantron, and check to be sure you have entered it correctly (or the computer will not give you credit for the exam) 1. Let φ : R 3 → R 3 be a smooth function. Which of the following is the 3form φ * ( dxdydz )? 2. Let φ : R 3 → R 3 be a smooth function. Suppose φ : Ω → M gives a parame terization of the region M ⊂ n by the region Ω ⊂ R n (i.e. M = φ (Ω) and the function is one to one outside a set with zero volume). Assuming φ preserves orientation (i.e. D ( φ ) has nonnegative determinant everywhere on Ω) what does integraldisplay Ω φ * ( dxdydz ) equal? (a) zero (by Stokes theorem) (b) The volume of the region M (this is the differential forms version of the change of variable formula) of the boundary of a given region Ω ⊂ R 3 (c) This is roughly the ratio of the volume of the image of a small box around a point to the volume of the box itself.a point to the volume of the box itself....
View
Full
Document
This note was uploaded on 09/18/2011 for the course M 427L taught by Professor Staff during the Spring '11 term at Oklahoma State.
 Spring '11
 staff

Click to edit the document details