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10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates to represent surfaces in space

10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates

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Page 1: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates

10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates)

Use cylindrical coordinates to represent surfaces in space

Use spherical coordinates to represent surfaces in space

Page 2: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates

CYLINDRICAL COORDINATES

Page 3: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates
Page 4: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates
Page 5: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates
Page 6: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates
Page 7: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates
Page 8: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates

SPHERICAL COORDINATES

Page 9: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates
Page 10: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates
Page 11: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates
Page 12: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates
Page 13: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates

Transform the point from spherical into

Cartesian coordinates.

Page 14: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates
Page 15: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates
Page 16: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates
Page 17: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates
Page 18: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates

Identify the surface:

**

Page 19: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates

Some generalizations about surfaces in spherical coordinates

Page 20: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates

Formulas that will be given to you!! Thanks Ms. Chen!!!

Page 21: 10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates

PG. 778 #1-65 ODD, 81-84Classwork/Homework