Complex Analysis [IAS (Admin.) Mains Mathematics]: Questions 1 - 7 of 39
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Question 1
Appeared in Year: 2016
Describe in Detail Subjective▾
Is is a harmonic function? Prove your claim. If yes, find its conjugate harmonic function and hence obtain the analytic function whose real and imaginary parts are and respectively. [CS (Main) Paper 2]
EditExplanation
- Given
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Question 2
Appeared in Year: 2016
Describe in Detail Subjective▾
Prove that every power series represents an analytic function inside its circle of convergence. [CS (Main) Paper 2]
EditExplanation
- Suppose
- Let be the radius of c…
… (495 more equations) …
Question 3
Appeared in Year: 2016
Describe in Detail Subjective▾
Let be the curve find, giving justifications, the value of the contour integral
[CS (Main) Paper 2]
EditExplanation
- Given represents a circle with radius 1.
Now
Let
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Question 4
Appeared in Year: 2012
Describe in Detail Subjective▾
Use Cauchy integral formula to evaluate , where is the circle . (CS main Paper 1)
EditExplanation
Cauchy integral formula for Higher Derivative:- If a function is analytic within and on a closed contour and in any point within then derivate of all orders are analytic and are given by.
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Question 5
Describe in Detail Subjective▾
Solve the following linear programing problem by the simplex method. Write its dual. Also, write the optimal table of the dual from the optimal table of the given problem:
Subject to:
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Question 6
Appeared in Year: 2011
Describe in Detail Subjective▾
Let be a Non-singular, square Matrix. Show that . Hence show that . (CS main Paper 1)
EditExplanation
Given be a Non-singular, square Matrix.
So, there exist of such that
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Question 7
Appeared in Year: 2012
Describe in Detail Subjective▾
Expand the function in Laurent series valid for
(CS main Paper 1)
EditExplanation
Given
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