1. 140410119100 - Jay Rami
140410119101 - Malhar Rana
140410119102 βRaval Harsh
140410119103 β Raval Parth
140410119104 β Ray Bhargav
2. ο Let f(z)be a continuous function of the complex
variable z=x+iy defined at every point of a
curve c whose end points are A and B divide
the curve c into n parts at the points
ο¨ A=P0(z0),P1(z1)β¦β¦..Pn(zn)=B
ο¨ Line integral of f(z) along the path C and is
denoted by π(π§) dz if c is a closed curve.
3.
4. Suppose that the equation z=z(t) represents the
contour c from point z=a to z=b also f(z) is
piecewise continuous on c then line integral or
contour integral of f along c in terms of
parameter of t is : c π(π§) dz = π(π§(π‘)).zβ(t)dt
Provided zβ(t) is piecewise continuous.
5. ο PROPERTIES OF LINE INTEGRALS:-
If F(z) and G(z) are integrable along a curve C
then the following properties hold:
1. Linearity
2. Sense reversal
3. Partitioning of path
4. Integral inequality
5. ML inequality
6. 1. Linearity:-
c [ π1π(π§)+k2 G(z)]dz=k1 c π(π§) dz +k2 c πΊ(π§)dz
For example:
7. 2. Sense reversal:-
π
π
π(π§)dz=- π
π
π(π§) dz
3.Patitioning of path:-
if the curve C consists of the curve c1 and c2
then:
π π(π§) dz = c1 π(π§)dz+c2 π(π§)dz
4. Integral inequality:
|c π(π§)dz|=< c |π(π§) ||dz|
8.
9.
10. 5. M L inequality:-
if F(Z)is continuos on the curve c of length L
and |f(Z)|=<M then:
|c π(π§)dz|=<ML