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1
Line Integral and Its Independence of the Path
±
This unit is based on Sections 9.8 & 9.9 , Chapter 9.
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All assigned readings and exercises are from the textbook
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Objectives
:
Make certain that you can define, and use in context, the terms,
concepts and formulas listed below:
1.
integrate a 2D or 3D vector field over a path.
2.
calculate the work done by a 2D or 3D force operating over a
path.
3.
dependence and independence of a line integral of the path
4.
conservative field and potential functions
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Reading
:
Read Section 9.8 & 9.9, pages .
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Exercises
:
Complete problems
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Prerequisites
: Before starting this Section you should
. . .
9
be familiar with the concept of integration
9
be familiar with vector algebra and partial derivatives
9
be familiar with 3D coordinate system
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Why line integrals?
±
The work
∆
W done by a force
F
in the
displacement of a particle along a curve
C (given by
r
(t)) a small distance
∆
d is:
r
F
r
r
F
d
F
W
r
r
r
r
r
r
r
∆
∆
∆
•
=
−
•
=
•
=
)
(
1
2
±
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This note was uploaded on 05/09/2010 for the course ENGR 233 taught by Professor S.samuelli during the Winter '10 term at Concordia Canada.
 Winter '10
 S.SamuelLi

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