Surface Integrals.

0:00 Introduction. 0:13 Surface Integrals. " f(x, y, z) = 1".

1:10 Compute the Surface Integral of the Double Integral of x^2 dS, where S is the unit Sphere x^2 +y^2 +z^2 = 1.

4:57 Any Surface S with Z = g(x, y) regarded as a parametric Surface with parametric equations: x = x, y=y, z = g(x, y). " Parameters: x, y ".

8:20 Evaluate the Double Integral of [y dS], where z = x + y^2; 0 " less than or equal" x " less than or equal" 1, 0 “less than or equal” y “ less than or equal" y " less than or equal" 2.

10:24 Evaluate the Double Integral of [z dS], where S is the Surface whose sides: S (1): the Cylinder x^2 +y^2 = 1 (SIDES). S(2): the disk x^2 + y^2 " is less than or equal to" 1 in the plane Z =0 (BOTTOM). S(3): the part of the plane z = 1+x that lies above S(2) (TOP ).

19:46 Surface Integrals of Vector Fields.

22:06 Find the FLUX of the vector field F (x, y,Z) = zi +yj + xk across the unit sphere x^2 +y^2 +z^2 =1.

29:05 The FLUX as a Concept.

29:32 In the case of a surface S given by a graph Z = g( x,y), we can think of "x" and "y" as PARAMETERS and use...

31:46 Evaluate the Double Integral of " F dot dS", where S is the boundary of the solid region "E" enclosed by the paraboloid z = 1-x^2 -y^2 and the plane z=0.