[h=2]CSS Applied Mathematics Past Paper 2010[/h]
[h=2]Applied Mathematics paper B 2010[/h]Applied Mathematics 2010Paper-II
Section A
Q. 1 Solve the following differential equations
a) y’’+5y’+6y = x
b) y’’+5yx = e^x
Q.2 (a) Derive Cachy-Riemann partial differential equations.
Q.2 (b) Derive Laplace Equation.
Q.3 (a)Yxx+ Yxy+Yyy = 4 e^3y
(b) u’’+6u’+9 = 0 ; u(0) = 2 ; u’(0) = 0
Section B
Q. 4(a) Discuss following
- Tensors
- ?ikj ?lmk
- Scalar fields for continuously differentiable function f=f(x,y,z)
Q.4(b) Can we call a vector as Tensor, discuss What is different between Vector and Tensor? What happens if we permute the subscript of tensors?
Q.5(a) Discuss the simplest and efficient method of finding the inverse of square matrix Aij of order 3×3.
Q.5(b) Apply any efficient method to compute the inverse of following Matrix
25 2 1
2 10 1
1 1 4
Section C
Q.6 (a) Develop Gauss-Seidel method for solving the linear System of equations of form
AX=B, where A is Coefficient matrix.
Q.6(a) Solve by Gauss-Seidel method following system of equation.
25X1 + 2X2 +X3 = 69
2X1+10X2+X3 = 63
X1+2X2+X3= 43
Q.7(a) Derive Simpsons Formula for the f(x) under limits x=a to x=6 as subintervals. (i-e) steps.
Q.7(b) solve by the Simpson formula
; integral (o to 1) 1/(1+x2)
Q.8(a) Derive Lagrange’s Formula upto four points.
Q.8(b) A curve passes through the following points
(0,1);(1,2);(2,5);(3,10) . Apply Lagrange formula to interpolate the polynomial.
[h=2]CSS (Applied Mathematics) Paper II (Optional)[/h]
[h=2]Applied Mathematics paper B 2010[/h]Applied Mathematics 2010Paper-II
Section A
Q. 1 Solve the following differential equations
a) y’’+5y’+6y = x
b) y’’+5yx = e^x
Q.2 (a) Derive Cachy-Riemann partial differential equations.
Q.2 (b) Derive Laplace Equation.
Q.3 (a)Yxx+ Yxy+Yyy = 4 e^3y
(b) u’’+6u’+9 = 0 ; u(0) = 2 ; u’(0) = 0
Section B
Q. 4(a) Discuss following
- Tensors
- ?ikj ?lmk
- Scalar fields for continuously differentiable function f=f(x,y,z)
Q.4(b) Can we call a vector as Tensor, discuss What is different between Vector and Tensor? What happens if we permute the subscript of tensors?
Q.5(a) Discuss the simplest and efficient method of finding the inverse of square matrix Aij of order 3×3.
Q.5(b) Apply any efficient method to compute the inverse of following Matrix
25 2 1
2 10 1
1 1 4
Section C
Q.6 (a) Develop Gauss-Seidel method for solving the linear System of equations of form
AX=B, where A is Coefficient matrix.
Q.6(a) Solve by Gauss-Seidel method following system of equation.
25X1 + 2X2 +X3 = 69
2X1+10X2+X3 = 63
X1+2X2+X3= 43
Q.7(a) Derive Simpsons Formula for the f(x) under limits x=a to x=6 as subintervals. (i-e) steps.
Q.7(b) solve by the Simpson formula
; integral (o to 1) 1/(1+x2)
Q.8(a) Derive Lagrange’s Formula upto four points.
Q.8(b) A curve passes through the following points
(0,1);(1,2);(2,5);(3,10) . Apply Lagrange formula to interpolate the polynomial.
[h=2]CSS (Applied Mathematics) Paper II (Optional)[/h]