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10. Thesis Title
by
A. U. Thor
B.S., University of California (1980)
S.M., Massachusetts Institute of Technology (1984)
Submitted to the Department of Electrical Engineering and Computer Science
in partial ful…llment of the requirements for the degrees of
Doctor of Philosophy
and
Master of Science
at the
UNIVERSITY OF NEW MEXICO
June 1999
c Remove to use default copyright from the style
The author hereby grants to University of New Mexico permission to reproduce and
to distribute copies of this thesis document in whole or in part.
Signature of Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Electrical Engineering and Computer Science
13 May 1998
Certi…ed by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
David Collis
Director, Sound and Furry Laboratory
Research Head
Certi…ed by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
George D. Pearson
Director, Technical Support
Thesis Supervisor
Accepted by. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Arthur C. Clarke
Chairperson, Department Committee on Graduate Students

11. Thesis Title
by
A. U. Thor
Submitted to the Department of Electrical Engineering and Computer Science
on 13 May 1998, in partial ful…llment of the
requirements for the degrees of
Doctor of Philosophy
and
Master of Science
Abstract
Replace with the thesis abstract
Research Head: David Collis
Title: Director, Sound and Furry Laboratory
Thesis Supervisor: George D. Pearson
Title: Director, Technical Support
2

12. Chapter 1
Mcqs(Lecture#1)
1.1 Choose the correct option-
1-Which is a curve?
(a)Line
(b)Parabola
(c)Circle
(d)All
2-Which of the following is not curved?
(a)Circle
(b)Line
(c)Parabola
(d)None
3-If a curve is smooth then:
(a)It has unique tangent at one point
(b)It has more than one tangent at each point
(c)It has unique tangent at each point
(d)None
4-If a function is continous but not di¤erentiable then the function is:
(a)Smooth function
(b)Non-smooth function
3

13. (c)None
5-If we are given with a curve (t) = t; t2; 1 + t2 ;then:
(a) (t) is smooth
(b) (t) is non smooth
(c)Both are not true
6-Which one is non smooth curve?
(a) (t) = (t; t3)
(b) (t) = (cos t; sin t)
(c) (t) = (t; jtj)
(d) (t) = t 1; t
7-A parameterization curve in Rn is a map : ( ; ) ! Rn; for some ; with:
(a) 1 < 1
(b)0 1
(c) 1 1
(d) 1 < 1
8-The parameterization of a straight line y = x is:
(a) (t) = t; 2t2
(b) (t) = (cos t; sin t)
(c) (t) = (t; t)
(d)All
9-If we are given with parametric equations x = 3 cos t and y = 3 sin t then it represents:
(a)Line
(b)Circle
(c)Parabola
(d)Hyperbola
10-For transidental paramrterization of a circle ,we take (t) = (cos t; sin t) with:
(a)t 2 [0; 1)
(b)t 2 [0; 2 )
(c)t 2 ( 1; 1)
(d)t 2 [0; 2 ]
4
(Its answer is d)

14. 11-If the tangent vector of a parameterized curve is constant then the image of the curve is:
(a)Any curved surface
(b)Hyperbola
(c)Straight line
(d)Parabola
1.2 Key:
1-(d) 2-(b) 3-(c) 4-(b) 5-(a)
6-(c) 7-(c) 8-(c) 9-(b) 10-(d)
11-(c).
5

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