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Understanding Vector-Valued Functions in Calculus III

Explore vector-valued functions using examples such as airplane flight paths and intersections of planes and spheres, understanding curves, shapes, lengths, and limits in calculus. Learn to parametrize curves and understand relationships with different geometric shapes.

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Understanding Vector-Valued Functions in Calculus III

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  1. Calculus III13.1 Vector-Valued Functions Friday September 23, 2016 Concordia College

  2. Example 1: Airplane Flight Path,Vectors Indicating Position

  3. Example 1: Airplane Flight Path,Vectors Indicating Position

  4. Definition:Vector-Valued Function

  5. Example 2

  6. Example 2

  7. Example 2

  8. Example 3

  9. Example 3

  10. Example 4

  11. Example 4

  12. Example 5: Matching

  13. Example 6Intersection of Cone and Plane

  14. Example 7 Parametrize the intersection of the plane with the sphere

  15. Example 7 Parametrize the intersection of the plane with the sphere

  16. Example8 Describe the curve and its projections onto the xy-plane and the yz-plane. Find a circular paraboloid on which the curve lies.

  17. Example 8

  18. Example9 Show that the graph of Lies on both a circular cylinder and a plane. What shape is it? Find the length of the major and minor axes.

  19. Example 9: Picture

  20. 10. Particle Collision

  21. 11. Limits

  22. 12. Example

  23. 13. Continuity

  24. 14. Theorem on Continuity

  25. 15. Example

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