Mathematical Methods of Physics-Elements of Complex Analysis (CSIR Physical Sciences): Questions 1 - 4 of 4

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Question number: 1

» Mathematical Methods of Physics » Elements of Complex Analysis

Appeared in Year: 2013

MCQ▾

Question

Which of the following functions cannot be the real part of a complex analytic function of z=x+iy ? (December)

Choices

Choice (4) Response

a.

3x2yyy3

b.

x2y

c.

x33xy2

d.

x2y2

Question number: 2

» Mathematical Methods of Physics » Elements of Complex Analysis

Appeared in Year: 2012

MCQ▾

Question

Let u(x,y)=x+12(x2y2) be the real part of an analytic function f(z) of the complex variable z=x+iy , the imaginary part of f(z) is – (June)

Choices

Choice (4) Response

a.

y2x2

b.

y+xy

c.

y

d.

xy

Question number: 3

» Mathematical Methods of Physics » Elements of Complex Analysis

Appeared in Year: 2014

MCQ▾

Question

Consider the function f(z)=1zln(1z) of a complex variable z=reiθ(r0,<θ<) . The singularities of f(z) are as follows: (December)

Choices

Choice (4) Response

a.

branch points at z=1 and z= ; and a pole at z=0 for all θ .

b.

branch points at z=0,z=1 and z=

c.

branch points at z=1 and z= ; and a pole at z=0 for all θ other than 0θ<2π

d.

branch points at z=1 and z= ; and a pole at z=0 only for 0θ<2π .

Question number: 4

» Mathematical Methods of Physics » Elements of Complex Analysis

Appeared in Year: 2014

MCQ▾

Question

The function Φ(x,y,z,t)=cos(zvt)+Re(sin(x+iy)) satisfies the equation (June)

Choices

Choice (4) Response

a.

1V22Φt2=(2x2+2y2+2z2)Φ

b.

(1V22t2+2z2)Φ=(2x2+2y2)Φ

c.

(1V22t22z2)Φ=(2x2+2y2)Φ

d.

(2z21V22t2)Φ=(2x2+2y2)Φ

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