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: 1. (a) (4 points) Consider the function f : R 2 R 2 dened f r = r cos r sin Compute the Jacobian [ Df ] = h df i dx j i i,j . Solution : [ Df ] = df i dx j i,j = " df 1 dx 1 df 1 dx 2 df 2 dx 1 df 2 dx 2 # = cos r sin sin r cos (b) (4 points) Suppose the inputs are h r, i = h 1 , 2 i and the rates of change of the inputs are h r, i = h , 4 i . Find the rates of change of the outputs. Solution : Df 1 2 r = 1 1 4 = 4 Let x = r cos and y = r sin . Then x =4 and y = 0. 2. (2 points) Write at least one thing you learned from the midterm last week. Solution : Exams can be learning experiences just like homework and quizzes! What did you learn?...
View
Full
Document
 Spring '07
 Cremins
 Calculus, Linear Algebra, Algebra

Click to edit the document details