STUPIDSID
1(a)
Evaluate the following:
3 M
1(b)
Solve (D4+4)y=0
3 M
1(c)
Prove that E∇ = Δ =∇E
3 M
1(d)
Solve the following:
3 M
1(e)
Evaluate ∫∫r3drdθ over the regions between the circles r=2sinθ and r=4sinθ
4 M
1(f)
Evaluate the following:
4 M
2(a)
Solve (x3y4+x2y3+xy2+y)dx + (x4y3-x3y2-x2y+x)dy=0
6 M
2(b)
Change the order of integral and evaluate:
6 M
2(c)
Prove that:
8 M
3(a)
Evaluate the following:
6 M
3(b)
Find the area of one loop of the lemniscate r2=a2cos2θ
6 M
3(c)
Solve (D3+2D2+D)y = x2e3x+sin2x+2x
8 M
4(a)
Show that the length of the arc of the parabola y2=4ax cut off by the line 3y=8x is alog2+15/16
6 M
4(b)
Using the method of variation of parameters, solve:
6 M
4(c)
Compute y(0.2) given (dy/dx)+y+xy2=0,
y(0)=0, By taking h=0.1 using Runge-Kutta method of fourth order correct to 4 decimals.
8 M
5(a)
Solve the following:
6 M
5(b)
Solve (dy/dx)-2y=3ex,y(0)=0 using Taylor Series method. Find approximate value of y for x=0.1 and 0.2
6 M
5(c)
Evaluate
using Trapezoidal rule, Simpson's 1/3rd rule and Simpson's 3/8th rule. Compare the result with exact values.
using Trapezoidal rule, Simpson's 1/3rd rule and Simpson's 3/8th rule. Compare the result with exact values.
8 M
6(a)
The current in a circuit containing an inductance L, resistance R and a voltage Esinωt is given by L (di/dt)+Ri=E sinωt. If i=0 at t=0, find i.
6 M
6(b)
Evaluate ∫∫e(2x-3y)dxdy over the triangle bounded by x+y=1, x=1 and y=1
6 M
6(c)(1)
Find the volume of solid bounded by the surfaces y2=4ax, x2=4ay and the planes z=0, z=3.
4 M
6(c)(2)
Change to polar co-ordinates and evaluate:
4 M
More question papers from Applied Mathematics 2