Quiz

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Quiz 1 30/30 congratulations

• AL-AMER, AHMAD ADNAN MOHA
• AL-AGEELI, AHMAD IBRAHIM
• AL-GARNI, BANDAR HASSAN S
• AL-ARJANI, ALI SAEED ABDU
• AL-BUGMI, TURKI MAHDI SHA
• AL-BARAK, MUHAMMAD ABDUL
• AL-MARRI, ALI MUHAMMAD FA
• AL-HASAN, KHALED MUHAMMAD
• AL-MANSOUR, ABDUL-RHMAN M
• MAKKI, EMAD AHMAD MUHAMMA
• AL-MESHAL, SAMI MUHAMMAD

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MATLAB can find
1) a definite integral
syms x Int(x2, x, 0, 1)
2) an indefinite integral
syms x Int(x2, x)
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Groups
Group 1 Turki al bogmi Turad al hujile Ahmad
aquile Emad Makki
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Problem 1
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9.9 Line Integral Independent of the Path
Evaluate
.along the curve C between (-3,-3) and (3,3)
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Problem 2
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9.9 Line Integral Independent of the Path
Evaluate
.along the curve C between (-3,-3) and (3,3)
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Problem 3
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9.9 Line Integral Independent of the Path
Evaluate
.along the curve C between (-3,-3) and (3,3)
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The Integral has the
same value
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Under what condition the integral is independent
of the path
is independent of the path
is an exact differential
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Test for exact differential
is an exact differential
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Problem 4
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Which line integral is dependent of the path
A)
Example4
B)
HW 7
C)
Example3
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Problem 5
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Application (1)
Evaluate
.along the curve C between (-3,-3) and (4,4)
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Problem 6
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Application (2)
Evaluate
.along the curve C between (-3,-3) and (4,4)
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Exact differential
is an exact differential
There exists a function
Such that
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Theorem 9.8 Fundamental Theorem for Line Integral
Suppose there exists a function
such that that is,
is an exact differential. Then
depends on only the endpoints A and B
of the path C and
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Application (1)
Evaluate
.along the curve C between (-3,-3) and (4,4)
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How to find
Method 1
Which method ????? Easy step 1
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(No Transcript)
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Notation
If
Is independent of the path between the endpoints
A and B, then we write
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Theorem 9.10 Test for Path Independence
Is independent of the path
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How to find
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Conservative Vector Fields
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Conservative Vector Fields

• In a gradient force field F,
• The work done by the force upon a particle moving
  from position A to position B is the same for all
  paths.
• The work done by a force along a closed path is
  zero

• In a conservative field F,
• The law of conservation of mechanical energy
  holds.
• For a particale moving along a path in a
  conservative field,
• kinetic energy potential energy
  constant

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Conservative Vector Fields
9.9
9.7
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Conservative Vector Fields
Remarks (pp501) A frictional force such as air
resistance is neoconservative. Neoconservative
forces are dissipative in that their action
reduces kinetic energy without a corresponding
increase in potential energy. In other words, if
the work done depends on the path , then F is
neoconservative.
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9.9 Homework
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9.9 Homework
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9.9 Homework
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9.9 Homework
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9.9 Homework