T3Solutions

# T3Solutions - MATH 3705C Test 3 Solutions[Marks Questions...

This preview shows pages 1–2. Sign up to view the full content.

MATH 3705C Test 3 Solutions March 16, 2007 Questions 1-2 are multiple choice. Circle the correct answer. Only the answer will be marked. [Marks] 1. At x = 58, the Fourier sine series of f ( x )= ½ 2 ; 0 x< 2 0 ; 2 x 3 ¾ converges, to [4] (a) 1 (b) -1 (c) 0 (d) -2 (e) None of these Solution: (b) 2. The solution of the wave equation u xx = 1 9 u tt ; 0 <x< 2, which satis¯es the boundary [4] conditions u (0 ;t )= u (2 ;t )=0 ,isg ivenby u ( x; t )= 1 X n =1 sin ³ n¼x 2 ´ a n cos μ 3 n¼t 2 + b n sin μ 3 n¼t 2 ¶¸ : If u ( x; t ) satis¯es the initial conditions u ( x; 0) = 0 and u t ( x; 0) = 3 sin( ¼x ) ¡ sin(3 ¼x ), the coe±cients a n and b n are given by (a) b 2 =3 ;b 6 = ¡ 1 ;b n = 0 otherwise, and a n = 0 for all n ¸ 1. (b) b 2 = 1 ¼ ;b 6 = ¡ 1 9 ¼ ;b n = 0 otherwise, and a n =0fora ll n ¸ 1. (c) a 2 = ¡ 3 ;a 6 =1 ;a n = 0 otherwise, and b n = 0 for all n

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

T3Solutions - MATH 3705C Test 3 Solutions[Marks Questions...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online