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0:06:11

Evaluate 𝐼=∫ᵧ 𝑥𝑑𝑧, where ᵧ be the boundary of square [0,1]×[0,1] with 𝐶 considered as 𝑅².

0:15:16

Find ∫ ᤲ ᷝͥͥͥ ໋ ͥ(𝑧²+𝑧)𝑑𝑧 by choosing two different paths of integration & show that result are same

0:03:34

Evaluate the integral ∫𑀾 𝑧̅ 𝑑𝑧 where 𝐶 is the straight line from the point (1,0) to the point (1,1)

0:04:32

Evaluate ∫𑀾 𝑧̅ 𝑑𝑧 , from 𝑧 = 0 to 𝑧 = 4+2𝑖 along the curve 𝐶 given by 𝑧 = 𝑡² + 𝑖𝑡 .

0:05:40

Prove ∫𑀾 𝑧̅𝑑𝑧 along semi-circular arc of |𝑧|=1 from -1→1 is -𝑖𝝅/𝑖𝝅 according above/below real axis.

0:05:47

Prove ∫𑀾 𝑑𝑧/𝑧 along semi-circular arc of |𝑧|=1 from -1→1 is -𝑖𝝅/𝑖𝝅 according above/below real axis.

0:05:38

Evaluate the integral 𝐼=∫𑀾 𝑅𝑒𝑧 𝑑𝑧 , on the circle |𝑧|=𝑟 .

0:05:57

Evaluate ∫𑀾 |𝑧| 𝑑𝑧 , where 𝐶 is the upper half of circle |𝑧|=1 .

0:06:16

Evaluate ∫𑀾 𝑧𝑑𝑧 .

0:03:12

Evaluate ∫𑀾 |𝑑𝑧| .

0:00:25

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0:00:18

Happy New Year 2023 🔥 | Stay Tuned | 🔥

0:03:29

Evaluate ∫𑀾 𝑑𝑧 in Complex Integration.

0:09:31

Define the Complex line integral.OR The Riemann's Definition of Integration in Complex Integration .

0:07:54

Rectifiable Curve in Complex Integration.

0:05:32

Continuous Jordan curve & Contour.

0:03:46

Jordan Arc and Regular Arc of Jordan Arc.

0:04:46

Continuous Arc and Multiple Point in Complex Integration.

0:03:47

Partition and Norm of the partition in Complex Integration ꯫𝑃꯫ .

0:09:24

Discuss the logarithmic transformation 𝑤=𝒍𝒐𝒈𝑧 .

0:24:08

Discuss the exponential transformation 𝑤=𝑒ᶻ .

0:07:27

Mapping 𝑤=𝑧² maps 𝐈 quadrant in 𝑧-plane bounded circles |𝑧|=𝑎,|𝑧|=𝑏 (𝑎≻𝑏≻0). Is mapping conformal ?

0:11:07

Show 𝑧=⎷𝑤 transform family of circles |𝑤-1|=𝑐 into family of lemniscate |𝑧-1||𝑧+1|=𝑐 (𝑐=parameter).