# PHY 312 Past Questions

**NATIONAL OPEN UNIVERSITY OF NIGERIA**

**University Village, Nnamdi Azikiwe Expressway, Plot 91, Cadastral Zone, Jabi, Abuja**

**FACULTY OF SCIENCE**

**2017_1 SEMESTER EXAMINATION**

**COURSE CODE: PHY 312**

**COURSE TITLE: MATHEMATICAL METHODS IN PHYSICS**

**MARKING GUIDE**

CREDIT UNIT: 3

TIME ALLOWED (3 HRS)

INSTRUCTION: Answer ONE and any 4 questions

**QUESTION 1**

a) State which of the following is an “even” function of t

i. t 3

ii. t 2

iii. cos(t)

iv. sin(t) (8 marks)

b) A sinusoidal voltage where t is time, is passed through a half-wave rectifier that clips the negative portion of

the wave. Sketch the resulting periodic function

(6 marks)

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**QUESTION 2**

a.The Bessel function is given by the series expansion:

Show that: (11 Mrks)

b. Determine the value of (3 Mrks)

**QUESTION 3**

State the generating function for the Hermite polynomials. (2 Mrks)

Given that:

Show that:

(6 Mrks)

b) For Laguerre’s polynomials, show that that . Assume the generating function:

(6 Mrks)

Hint: Put x = 0,

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**QUESTION 4**

Find the Fourier series of the periodic function defined by:

(14 Mrks)

**QUESTION 5**

a. Solve the equation , subject to the boundary conditions that at and at (11

Marks)

b. (i) State the Laguerre polynomial that is a solution of the Laguerre’s equation. (2Mrks)

ii Find (1Mrk)

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**QUESTION 6**

A bar of length 2m is fully insulated along its sides. It is initially at a uniform temperature of 10 °C and at t = 0 the

ends are plunged into ice and maintained at a temperature of 0°C . Determine an expression for the temperature at a

point P a distance x from one end at any subsequent time t seconds after t=0. (14 Mrks)

Hint: Use the heat equation with boundary conditions

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