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Advanced engineering Mathematics
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  • Course
  • Advanced engineering Mathematics
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  • Advanced Engineering Mathematics

1. Definition of the Com- plex Line integral 2. Complex line integral sum form 3. What is the line inte- gral of f(z) over the curve C by limit form? 4. What is the line inte- gral of f(z) over the curve C by integral form? 5. What is the meaning of complex line in- tegrals consist of fi- ...

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  • May 10, 2023
  • 20
  • 2022/2023
  • Exam (elaborations)
  • Questions & answers

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  • 1 definition of the com plex line integral 2 complex line integral sum form 3 what is the line inte gral of fz over the curve c by limit form 4 what is the line inte gral of fz ove

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  • Advanced engineering Mathematics
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Advanced engineering Mathematics
Study online at https://quizlet.com/_9v4qgx

1. Definition of the
1 . C has to be a smooth curve and f(z) has
Com- plex Line
to be a continuous function.
integral
2.We will subdivide the curve C by
points z0,z1,....,zn-1,zn = (Z)
3.Choose arbitrary point, between z0 - z1, z1 -
z2 etc.



2. Complex line
integral sum form

3. What is the line inte- the limit of the finite sum will be obtained as
gral of f(z) over the n goes to infinity.
curve C by limit
form?


4. What is the line inte-
gral of f(z) over the
curve C by integral
form?
If all paths of integration for complex line
5. What is the meaning integrals are assumed to be at least
of complex line in- piecewise smooth.
tegrals consist of fi-
nitely many smooth
curves?

6. Three basic proper-
1. linearity
ties of complex
2. Sense reversal
inte- gration
property 3.Partitioning
7. What is linearity of of path
in- tegration?
if there are 2 complex function having linear
opera- tion, then they can be integrated
8. What is sense separately.
rever- sal property?
1/

,Advanced engineering Mathematics
Study online at https://quizlet.com/_9v4qgx
changing their limit by adding minus sign




2/

, Advanced engineering Mathematics
Study online at https://quizlet.com/_9v4qgx
9. What is partitioning integrate function by 2 path which is one path
of path ? actually



10.What is existence of
the complex line If f(z) is continuous and the curve C is at least
inte- gral ? piece- wise smooth, the complex line integral
of f(z) exists
11.Proof of existence of
the complex line
inte- gral

12.What is first
method of solving
complex line Indefinite integration and substituition of
integral ? limits, but it is restricted to analytic
functions.
13.Theorem of indefinite
integration of
analytic functions If f(z) is analytic in a simply connected
domain D, In the domain there exists an
indefinite integral of f(z), F'(z) = f(z) and for
all paths in D joining two points z0 and z1
14.What is the second
method of solving
complex line
integral Use of a oarametric representation of the
? path, ap- plies to any continuous complex
function.
15.Theorem of integra-
tion by the use of a
parametric represen-
tation of the path If C be at least piecewise smooth, and
represented by z = z(t), where a<= t <=b.
16.Proof of integration f(z) be continuous on the C
by the use of a para-
metric representation
of the path
3/

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