Paul's Online Math Notes
[Notes]
Calculus III - Assignment Problems
 Applications of Partial Derivatives Previous Chapter Next Chapter Line Integrals Triple Integrals in Spherical Coordinates Previous Section Next Section Surface Area

Change of Variables

For problems 1  4 compute the Jacobian of each transformation.

1.

2.

3.

4.

5. If R is the region inside  determine the region we would get applying the transformation ,  to R.

6. If R is the triangle with vertices ,  and  determine the region we would get applying the transformation ,  to R.

7. If R is the parallelogram with vertices , ,  and  determine the region we would get applying the transformation ,  to R.

8. If R is the square defined by  and  determine the region we would get applying the transformation ,  to R.

9. If R is the parallelogram with vertices , ,  and  determine the region we would get applying the transformation ,  to R.

10. If R is the region bounded by , ,  and  determine the region we would get applying the transformation ,  to R.

11. Evaluate  where R is the region bounded by , ,  and  using the transformation , .

12. Evaluate  where R is the triangle with vertices ,  and  using the transformation ,  to R.

13. Evaluate  where R is the parallelogram with vertices , ,  and  using the transformation ,  to R.

14. Evaluate  where R is the region bounded by , ,  and  using the transformation , .

15. Evaluate  where R is the parallelogram with vertices , ,  and  using the transformation ,  to R.

16. Derive a transformation that will transform the ellipse  into a unit circle.

17. Derive the transformation used in problem 12.

18. Derive the transformation used in problem 13.

19. Derive a transformation that will convert the parallelogram with vertices , ,  and  into a rectangle in the uv system.

20. Derive a transformation that will convert the parallelogram with vertices , ,  and  into a rectangle with one corner occurring at the origin of the uv system.

 Triple Integrals in Spherical Coordinates Previous Section Next Section Surface Area Applications of Partial Derivatives Previous Chapter Next Chapter Line Integrals

[Notes]

 © 2003 - 2017 Paul Dawkins