Complex Analysis (B.Sc. Mathematics)
39 videos • 1,534 views • by Doctor of Mathematics
1
Evaluate integrate z^2 from 0 to 1+i w. r. t. z.
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2
Evaluate the integral e^iz/z^3 with respect to z along C :|z|=1.
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3
Evaluate closed line integration 1/z-2w.r t. z along the circle |z-2|=4.
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4
Cauchy's Integral Theorem or Cauchy Gaursat Theorem
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5
Evaluate dz/(z^2+9) , where C is circle |z-3i|=4.
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6
∫(4-3z)dz/(z^2-z) , where C is any simple closed path such that 1€C and0¢C.
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7
Evaluate ∫(z-3) /(z^2+2z+5) dz, where C is |z|=1.
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8
Find the residue of 1/(1+z^2)^n at z=i
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9
Find the residue of (1+e^z)/(sinz+z.cosz) at the pole z=0.
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10
Show that all singular point of 1/z(e^z-1) are poles. Find the order of poles and find the residue
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11
Evaluate ∫c(z^2+3z)dz alog the circle|z|=0 from (2,0) to (0, 2) in a counterclockwise direction.
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12
Evaluate ∫c(5z^4-z^3+2)dz around the circle |z|=1.||Best mathematics channel on YouTube
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13
Evaluate ∫c(5z^4-z^3+2)dz around the |z|=1,square (0, 0), (1, 0), (1, 1),(0, 1) ;along y=x^2 (0, 0)
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14
Evaluate ∫c(5z^4-z^3+2)dz around the square with vertices (0, 0), (1, 0), (1, 1) and (0, 1).TOP chan
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15
dz/dw=del z/del u (TOP mathematics channel on YouTube)
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16
Bilinear or Linear Fractional Transformation Definition || Top mathematics channel on YouTube
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17
Prove that the resultant of two bilinear transformation is a bilinear transformation. ||Top Maths
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18
Solve:(x+1)d^2y/dx^2-2(x+3)dy/dx+(x+5)y=e^x ||Top mathematics channel on YouTube
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19
Find the analytic function of which the real part is e^-x[(x^2-y^2)xcosy+2xysiny]
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20
Prove that tan-1(i x-a/x+a)=-i/2loga/x
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21
Find the integral of (2z-2)/(z^2-5z+6) along C where C is |z|=4. [Complex Analysis]
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22
Show that the function f(z)=xy^3/x^2+y^6, z≠0;f(0)=0, is not continuous at the origin.
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23
Find the bilinear transformation which maps z=2,1,0 respectively onto w=1,0,i.
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24
An Example of Rotation transformation|Consider the transformation w=ze^i/4 and determine the region
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25
Inversion Transformation|Conformal Mapping|Complex Analysis
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26
Use Cauchy's integral formula to evaluate ∫(z^2+1)/(z^2-1)dz Where C has radius 1 with centre at z=1
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27
Evaluate the integral ∫C1/z.coszdz, where C is the ellipse 9x^2+4y^2=1
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28
Consider the transformation w=2z and determine the region R' of w-plane into which the triangular re
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29
Find five terms in the Lauren's expansion of 1/z(e^z-1) for the region |z| greater than 0 and less
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30
Find the value of ∫Cdz/sinhz,where C is the circle |z|=4 described in the positive sense.
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31
Prove that the function |z|^2 is continuous every where but nowhere differwntiable except at the ori
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32
find the billinera transformation of the points which maps the points -1,0,1 onto the points 0,i, 3i
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33
Use Cauchy's integral formula to evaluate z/(z^2-3z+2)dz where C is a circle |z-2|=1/2.
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34
∫e^z/z^2(z+1)^3dz,C: |z|=2
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35
Separate real and imaginary parts of e^α+iβ.
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36
Show that the function f(z)=x-iy is not analytic at any point.
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37
Find all the roots of the equation x^5-1=0.
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38
If |2z-1|=|z-2|, prove that the point z=x+iy lies on the circle x^2+y^2=1.
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39
Expand f(z)=1/(z+1)(z+3) in a Laurent's series valid for the regions (i) 1 less than|z| leas rhan 3
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