Solve your IGNOU Doubts

Question:

Find the image of the circle | z | = $r(r\neq 1)$ under the mapping $w=f(z)=\frac{z-i}{z+i}$ . What happens when r = 1 ?

See Answer →

Question:

Using second order finite differences method with , $h = \frac{1}{2}$ obtain the system of equations for $y_{0^,} y_{1}$ and $y_{2}$ for solving the boundary value problem:

$y'' - 5y'+6y = 3$

with $y(0)-y'(0)=-1$ and $y(1)+y'(1)=1$

See Answer →

Question:

$I=\int_{0}^{2\pi }f(e^{i\theta })sin^{2} \theta /2 d\theta$

See Answer →

Question:

Evaluate the following integrals: $I=int_{0}^{2pi }f(e^{i heta })cos^{2}( heta /2)d heta .$

See Answer →

Question:

Find the points where the function $f(z)= frac{log(z+4)}{z^{2}+i}$ is not analytic.

See Answer →

Question:

Consider $f(z)=z^{2}-z$ and the closed circular region $R=left { z:left | z ight |\leq 1 ight }$ . Find points in R where | f (z)| has its maximum and minimum values

See Answer →

Question:

If f = u + iv is entire such that $u_{x}+v_{x}=0$ in $mathbb{C}$ then show that f has the form f (z) = az + b where a, b are constants with Rea = 0 .

See Answer →

Question:

Heat conduction equation $u_{1} = u_{xx}$ is approximated by the method:

$u_{m}^{n+1}-u_{m}^{n-1} = frac{2k}{h^2}delta_{k}^{2} u_{m^.}^{n}$

Find the order of the method and investigate the stability of this method using Von Neumann method.

See Answer →

Question:

Evaluate , $L^{-1}left { frac{1}{(s+1)(s^2+1)} ight },$ using convolution theorem.

See Answer →

Question:

Find the solution of $Delta^2u = 0$ in R subject to R : triangle $0 leq x leq1,0 leq y leq 1, 0leq x+yleq 1$ and $u(x,y) = x^2 - y^2$ on the boundary of the triangle. Assume 4 $h=frac{1}{4}$ and use five-point formula.