Uthm Final Exam

4376 Words18 Pages
CONFIDENTIAL UNIVERSITI TUN HUSSEIN ONN MALAYSIA FINAL EXAMINATION SEMESTER I SESSION 2011/2012 COURSE NAME COURSE CODE PROGRAMME : : : ENGINEERING MATHEMATICS IV BWM 30603/BSM 3913 1 BEE 2 BDD/BEE/BFF 3 BDD/BEE/BFF 4 BDD/ BFF JANUARY 2012 3 HOURS ANSWER ALL QUESTIONS IN PART A AND TWO (2) QUESTIONS IN PART B. ALL CALCULATIONS AND ANSWERS MUST BE IN THREE (3) DECIMAL PLACES. EXAMINATION DATE : DURATION INSTRUCTION : : THIS EXAMINATION PAPER CONSISTS OF SEVEN (7) PAGES CONFIDENTIAL BWM 30603 /BSM 3913 PART A Q1 (a) Consider the heat conduction equation  2 T ( x, t )   2 T ( x, t ), t x 0  x  10, t  0 , where  is thermal diffusity  10, since   c 2 . Given the boundary conditions, T (0, t )  0, T (10, t )  100 and…show more content…
If p(0)  0.01, b  0.02 and r  0.1 , approximate p(3) by using secondorder Taylor series method and modified Euler’s method. Assume that h  t  1 year. (ii) Solve the following boundary value problem y   4 y   4 y  et , y(0)  0, y(1)  0 . Consider h  t  0.25 . (17 marks) 5 BWM 30603 /BSM 3913 FINAL EXAMINATION SEMESTER / SESSION: SEM I/ 2011/2012 COURSE :ENGINEERING MATHEMATICS IV PROGRAMME : 1/2/3/4 BDD/BEE/BFF CODE : BWM 30603/ BSM 3913 FORMULAS Nonlinear equations Secant method : xi  2  xi f ( xi 1 )  xi 1 f ( xi ) f ( xi 1 )  f ( xi ) System of linear equations Gauss-Seidel iteration method: xi ( k 1)  bi   aij x j ( k 1)  j 1 i 1 j i 1 a x ij n (k ) j aii , i  1, 2, ,n Interpolation Lagrange polynomial: Pn ( x)   Li ( x) f ( xi ), i  0,1, 2, i 0 n , n where Li ( x)   j 0 j i n (x  x j ) ( xi  x j ) Newton divided difference: Pn ( x)  f0[0]  f 0[1] ( x  x0 )  f0[2] ( x  x0 )( x  x1 )   f 0[ n] ( x  x0 )( x  x1 ) ( x  xn1 ) Numerical differentiation and integration Integration: Gauss quadrature: For  b a f ( x)dx , x (b  a)t  (b  a) 2 3-points:  1 1 f ( x)dx  5  3 8 5  3 g    g  0 

    More about Uthm Final Exam

      Open Document