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CHAPTER 3 – COMPLEX INTEGRATION .

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CHAPTER 3 – COMPLEX INTEGRATION .


2marks :

1.  State Cauchy’s Integral theorem (OR) Cauchy’s Fundamental theorem .

2.  State Cauchy’s Integral theorem Formula.

3.  State Cauchy’s Integral Formula for derivatives.

4.  Simple Problems using Cauchy’s Integral Formula.

5.  State Taylor’s series.

6.  State Laurent’s Series.

7.  Simple Problems using Taylor’s & Laurent Series.

8.  Define Singular Point.

9.  Define Isolated Singularity . Give an example.

10.  Define Essential Singularity. Give an example.

11.  Define Removable Singularity. Give an example.

12.  Define Residue at a Pole.

13.  Define Pole & its type.

14.   State Cauchy’s Residue Theorem.

15.   Simple Problems Using Cauchy’s Residue Theorem.

16.  What is analytic & Principal part of Laurent’s Series.

17.  What are the poles of cot z ?

18.  Define Mesomorphic Function.

19.  Define Simply & multiply Connected Region.

20.  What are the formula’s to find the residue of a function at a simple pole ?


21.   State Contour Integral.
22.   Simple Problems Using Zeroes & Poles.

23.   State Cauchy’s extended theorem for Multiply Connected Region.

24.  What are the formula’s to find the residue of a function at multiple pole ?

25.   Evaluate ______ where C is the circle |z| = _____.

26.Simple Problems Using “FIND WHICH SINGULARITY IT BELONGS.” ?

27.  Find the Taylor’s series expansion of sin z in about z = pi / 4

28. Find the residue of cot z at the pole z=0.

29.Explain the term singularity.


Note :

·         “ _____ “ implies that model problem will come “

·         In Cauchy’s Integral Formula ,if a point lies outside the given region , then it’s value become zero.




15 Marks :

(You can Omit Atmost one Part Mentioned Below)

PART 1 – Cauchy’s Integral Theorem (Problem’s + Proof )

PART 2 – Cauchy’s Residue Theorem  (Problem’s + Proof )

PART 3 – Contour Integration. (Problem’s + Proof )

PART 4 -  Laurent’s series ( Problem’s)

Part 5 –   Taylor’s Series. ( Problem’s ) 


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