Ma 242 003
Download
1 / 58

MA 242.003 - PowerPoint PPT Presentation


  • 86 Views
  • Uploaded on

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 .

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' MA 242.003 ' - maura


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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




Recall the following from chapter 10 on parametric CURVES:

Example:


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.



My standard picture of a curve:

Parameterized curves are 1-dimensional.


My standard picture of a curve:

Parameterized curves are 1-dimensional.

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





We will work with two types of surfaces:

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


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


First consider Type 1 surfaces that are graphs of functions of two variables.


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.


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.


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.


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.


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.


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)>


General Rule:

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

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


General Rule:

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

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


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


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

Spheres


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

Spheres

Cylinders


2. Transformation Equations



Each parametric surface has a u-v COORDINATE GRID on the surface!


Each parametric surface has a u-v COORDINATE GRID on the surface!


Each parametric surface has a u-v COORDINATE GRID on the surface!

r(u,v)


ad