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Physics — Unit 1 — Test 9

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Cutoff (GEN): 70%

1/10

1

Cauchy’s integral theorem applies if

A

Function is non-differentiable

B

Function has poles inside contour

C

Function is analytic

D

Function is real only

2

Laurent series expansion is useful around

A

Real axis only

B

Ordinary points

C

Singularities

D

Infinity only

3

If a function has a simple pole at z₀

A

then residue is

B

Limit (z→z₀)(z−z₀)f(z)

C

Integral along real axis

D

Derivative at z₀

4

Residue theorem is useful in evaluating

A

Indefinite integrals

B

Definite integrals

C

Ordinary differential equations

D

Series expansions

5

Fourier series represents a function as

A

Sum of exponentials only

B

Sum of polynomials

C

Sum of trigonometric terms

D

Product of functions

6

For Fourier series

A

orthogonality is between

B

Exponential & polynomial functions

C

Legendre & Bessel functions

D

Sine & Cosine functions

7

Differential equation satisfied by Legendre polynomials is

A

(1+x²)y''+y=0

B

y''+y=0

C

y''+xy=0

D

(1−x²)y''−2xy'+n(n+1)y=0

8

Hermite polynomials satisfy differential equation

A

y''+y=0

B

y''−xy=0

C

y''+xy=0

D

y''−2xy'+2ny=0

9

Bessel’s equation is

A

x²y''+xy'+(x²−n²)y=0

B

(1−x²)y''+y=0

C

y''+xy=0

D

y''+y=0

10

Gamma function Γ(n) for positive integer n equals

A

n!

B

(n−1)!

C

n²

D

1/n

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