Math 1350
Review Topics for the Midterm Exam
Denitions
Smooth curve
Regular curve
Unit Tangent, principal normal, binormal vectors
Curvature and torsion
Signed curvature
Rigid motion
Dieomorphism
Derivative (aka Jacobian) matrix
Coordinate patch
Smooth su
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Math 1350
Solutions to Homework 4
March 23, 2010
4.2 There are many ways to do this. Heres one. Let U = R2 \ cfw_(0, 0). Dene
(u, v ) =
u
v
1
,
, ln(u2 + v 2 ) .
2
2 + v2 2
+v
u
u2
Then maps U into S . To see that its bijective, note that the map
: S U
Homework 2 Solutions
February 12, 2010
1. Let v1 , . . . , vn1 Rn , where n 2. Recall that the cross product
v1 vn1 is dened by
v1 vn1 , x = det[v1 vn1 x]
for every x Rn .
(a) Let v1 , . . . , vn1 Rn . Show that v1 vn1 is orthogonal to
each vj .
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Math 1350 Midterm Exam
February 25, 2010
Name:
Instructions: No books or notes may be used during the exam. Attempt all problems, giving complete and clear explanations of your answers.
1. (10 points each) State and prove each of the following:
(a) The Py
Math 1350 Midterm Exam Solutions
February 25, 2010
Instructions: No books or notes may be used during the exam. Attempt all problems, giving complete and clear explanations of your answers.
1. (10 points each) State and prove each of the following:
(a) Th