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