Probability and complex function: Unit IV: Complex integration

Problems based on contour integration (Method 2)

Solved Example Problems

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Probability and complex function: Unit IV: Complex integration : Problems based on contour integration

PROBLEMS BASED ON CONTOUR INTEGRATION

Example 4.4.2.

[Anna, May 2001] [A.U N/D 2007] [AU M/J 2009] [A.U N/D 2005, N/D 2008, M/J 2013] [A.U A/M 2017 R-08] [A.U A/M 2019 R-13] [A.U A/M 2019 R-8]

Solution :

Consider where C is the upper half of the semi-circle r with the bounding diameter [-R, R].

Example 4.4.5(a)

Solution:

See Example 4.4.5

Example 4.4.6(a) Evaluate

Solution :

See Example 4.4.6

Example 4.4.8

Solution:

where C is the upper half of the semi-circle I with the bounding diameter [-R, R]

Type III

TYPE 4

Integrals of the type where F(x) has zeros on the real axis.

The singularities on the real axis are enclosed in small semi-circle to avoid their inclusions in C, i.e., the contour C is indented at these singularities.

IX. Problems based on integrals of the type

where F(x) has zeros on the real axis.

Example 4.4.12. Show that

Solution :

Probability and complex function: Unit IV: Complex integration : Tag: : Solved Example Problems - Problems based on contour integration (Method 2)

Home | Department: EEE Department | Subject: Probability and complex function |

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