Parametric Surfaces and their Area.

0:00 Introduction.

0:11 Parametric Surfaces and their Area.

2:19 Find a parametric representation of the sphere x^2 + y^2 + z^2 = a^2.

5:38 Find a parametric representation for the Cylinder: x^2 +y^2 = 4 0" less than or equal to" z less than or equal to" 1. 7:14 Find a parametric representation for the Surface z = 2 SRT ( x^2 +y^2), that is, the top half of the Cone Z^2 = 4x^2 +4 Y^2. 9:54 Tangent Planes.

17:06 Find the tangent plane to the surface with parametric equations; x = u^2, y = v^2, z = u +2v at the point (1, 1, 3).

20:15 Surface Area. 26:00 Definition of the Surface Area.

27:11 Find the Surface Area of a Sphere of radius a.

32:20 Surface Area of the graph of a function. " Specifying the parameters". Very important Formula for A(S).

34:38 Find the area of the part of the paraboloid Z = x^2 +y^2 that lies under the plane z = 9.