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Name
Reg No
A
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
07 THRISSUR CLUSTER
FIRST SEMESTER M.TECH. DEGREE EXAMINATION DEC 2017
Mechanical Engineering
Thermal Engineering
07ME6401 COMPUTATIONAL MATHEMATICS
Time 3 hours Max. Marks: 60
Answer all six questions. Part of each question is compulsory.
Answer either part or part of each question
Q.no. Module 1 Marks
1a Solve x2 q z2 4
Answer b or c
b Derive one dimensional wave equation. 5
c Classify x2uxx 5
Q.no. Module 2 Marks
2a Using Taylors series method evaluate if
4
Answer b or c
b Using Runge-Kutta method evaluate if
5
c Using Euler's method evaluate y(.2)and if
5
Q.no. Module 3 Marks
3a Show that
4
Answer b or c
b Derive Rodrigue's formula 5
c Express 5x3+x in terms of Legendre polynomial 5
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Q.no. Module 4 Marks
4a Explain errors in discretization 4
Answer b or c
b Explain Tri-Diagonal Matrix Algorithm applied to Dimensional Problem 5
c Describe fully explicit, Crank-Nicolson and fully implicit schemes of
Discretisation
5
Q.no. Module 5 Marks
5a Show that δi
j is a mixed tensor of order two. 5
Answer b or c
b A covariant tensor has component xy, 2y-z2 ,xz in rectangular co-ordinates.
Find its covariant components in spherical co-ordinates
7
c Determine the metric tensor, conjugate metric tensor in cylindrical coordinates 7
Q.no. Module 6 Marks
6a Derive elemental matrix from elemental strain energy 5
Answer b or c
b Explain isoparametric, sub parametric super parametric elements. 7
c Explain the different steps involved in Finite Element Analysis 7