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MA 242.003 . Day 58 – April 9, 2013. MA 242.003 . The material we will cover before test #4 is:. MA 242.003 . Section 10.5: Parametric surfaces. MA 242.003 . Section 10.5: Parametric surfaces Pages 777-778: Tangent planes to parametric surfaces. MA 242.003 .

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ma 242 003
MA 242.003
  • Day 58 – April 9, 2013
ma 242 0031
MA 242.003

The material we will cover before test #4 is:

ma 242 0032
MA 242.003
  • Section 10.5: Parametric surfaces
ma 242 0033
MA 242.003
  • Section 10.5: Parametric surfaces
  • Pages 777-778: Tangent planes to parametric surfaces
ma 242 0034
MA 242.003
  • Section 10.5: Parametric surfaces
  • Pages 777-778: Tangent planes to parametric surfaces
  • Section 12.6: Surface area of parametric surfaces
ma 242 0035
MA 242.003
  • Section 10.5: Parametric surfaces
  • Pages 777-778: Tangent planes to parametric surfaces
  • Section 12.6: Surface area of parametric surfaces
  • Section 13.6: Surface integrals
slide10

Space curves

DEFINITION: A space curve is the set of points given by the ENDPOINTS of the Vector-valued function

when the vector is in position vector representation.

slide14

My standard picture of a curve:

Parameterized curves are 1-dimensional.

slide15

My standard picture of a curve:

Parameterized curves are 1-dimensional.

We generalize to parameterized surfaces, which are 2-dimensional.

slide22

We will work with two types of surfaces:

Type 1: Surfaces that are graphs of functions of two variables

slide23

We will work with two types of surfaces:

Type 1: Surfaces that are graphs of functions of two variables

Type 2: Surfaces that are NOTgraphs of functions of two variables

slide25

An example: Let S be the surface that is the portion of

that lies above the unit square x = 0..1, y = 0..1 in the first octant.

slide26

An example: Let S be the surface that is the portion of

that lies above the unit square x = 0..1, y = 0..1 in the first octant.

slide27

An example: Let S be the surface that is the portion of

that lies above the unit square x = 0..1, y = 0..1 in the first octant.

slide28

An example: Let S be the surface that is the portion of

that lies above the unit square x = 0..1, y = 0..1 in the first octant.

slide29

An example: Let S be the surface that is the portion of

that lies above the unit square x = 0..1, y = 0..1 in the first octant.

slide30

An example: Let S be the surface that is the portion of

that lies above the unit square x = 0..1, y = 0..1 in the first octant.

General Rule

If S is given by z = f(x,y) then

r(u,v) = <u, v, f(u,v)>

slide32

General Rule:

If S is given by y = g(x,z) then

r(u,v) = (u,g(u,v),v)

slide34

General Rule:

If S is given by x = h(y,z) then

r(u,v) = (h(u,v),u,v)

slide36

Consider next Type 2 surfaces that are NOT graphs of functions of two variables.

Spheres

slide37

Consider next Type 2 surfaces that are NOT graphs of functions of two variables.

Spheres

Cylinders

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