This presentation was done at KUSEOD.

1. Welcome
On the PresentationOn the Presentation
Niroj Dahal
School of Education
2011 Feb. Batch

2. Problem 2
(a).
Here,
z=r2
For Cartesian Co-ordinate
z=(x2+y2)2 [r2=x2+y2]z=(x +y ) [r =x +y ]
Or, x4+x2y2+y4=z
For spherical Co-ordinate
z=r2
Or, = ( )2 [z= and r= ]
=
φρsinρ
ρ
φ
φ
2
sin
cos
φcos φρ cos φρsin
∴

3. Maple Plot Command:
(a)with(plots):
> rho:=(phi)-> cos(phi)/sin^2 (phi);
> sphereplot([rho(phi),theta,
:=ρ →φ
( )cos φ
( )sin φ 2
> sphereplot([rho(phi),theta,
phi],theta=0..2*Pi, phi=0..Pi,axes=normal);

4. Figure

5. Continue
implicitplot3d(x^4+2*x^2*y^2+y^4=z,
x=4..4,y=-4..4,z=1..5);

6. Continue…
>Cylinderplot ([r,theta,r^2],r=-2..2, theta=0..2*Pi);
Figure

7. b.
(b).
Here,
For Cartesian Co-ordinate
[Multiplying both side by r]
Or, x2+y2= 4x [r2=x2+y2 and ]
θcos4=r
θcos42
rr =
θcosrx =Or, x +y = 4x [r =x +y and ]
Or, x2+y2-4x=0
For spherical Co-ordinate
[Putting ]
Or,
θφρ cos4sin = φρsin=r
φ
θ
ρ
sin
cos4
=

8. Maple Plot Command:
(b)
> restart:
> with(plots):
rho:=(theta,phi)-> 4*cos (theta)/sin(phi);rho:=(theta,phi)-> 4*cos (theta)/sin(phi);
> sphereplot([rho(theta, phi),theta,
phi],theta=0..2*Pi, phi=0..Pi,axes=normal);
:=ρ →( ),θ φ 4
( )cos θ
( )sin φ

9. Figure

10. Continue…
> plot3d(x^2+y^2-4*x, x=-4..4,y=-4..4);

11. Continue..
>cylinderplot([4*cos(theta),theta, z], z=-2..2, theta=0..2*Pi);

12. c.
(c).
Here,
r2+z2=4, z < -2
For Cartesian Co-ordinate
x2 + y2+z2=4 [r2=x2+y2] as z < -2
For spherical Co-ordinateFor spherical Co-ordinate
Putting
Or,
Or,
Or,
as z < -2 so < 2
φρφρ cos,sin == zr
2
4
4)cos(sin
4)cos()sin(
2
222
22
=
=
=+
=+
ρ
ρ
φφρ
φρφρ
ρΘ

13. Maple Plot Command with figure
(c)> restarts:
> with(plots):
> Sphereplot ([2,theta, phi],theta=0..2*Pi,
phi=0..Pi,axes=normal);

14. Continue…
>cylinderplot([sqrt(4-z^2),theta,z],z=-2..2, theta=0..2*Pi);

15. Continue..
> implicitplot3d(x^2+y^2+z^2=4, x=-4..4, y=-2..3, z=1..3);

16. d.
(d).
Here,
Or,
Or,
Or,
For Cartesian Co-ordinate
0sincos
0)sin(cos
02cos
2222
222
2
=−+
=−+
=+
θθ
θθ
θ
rrz
rz
rz
For Cartesian Co-ordinate
Putting
z+x2-y2=0
x2-y2 +z=0
θθ sin,cos ryrx ==
Θ

17. Continue..
For spherical Co-ordinate
Putting
Or,
θφρφ
θφρφρ
φρφρ
02cossincos
02cossincos
cos,sin
2
22
=+
=+
== zr
Or,
θφ
φ
ρ
θφρφ
2cossin
cos
02cossincos
2
2
−
=
=+
Θ

18. Maple Plot Command :
(d)> restarts:
> with(plots):
> rho:=(theta,phi)-> -cos(theta)/(sin(phi)^2*cos(2*theta));
:=ρ →( ),θ φ −
( )cos θ
> Sphereplot ([rho(theta, phi),theta, phi],theta=0..2*Pi,
phi=0..Pi,axes=normal);
:=ρ →( ),θ φ −
( )sin φ 2
( )cos 2 θ

19. Figure

20. Continue…
>cylinderplot([r,theta,-r^2*cos(2*theta)],r=-2..2,
theta=0..2*Pi);

21. Continue..
> implicitplot3d(x^2+y^2+z^2=4, x=-4..4, y=-2..2, z=1..2);

22. Thank You