1. Transformations

2. Left boundary of S maps to r(u0,v)
Lower boundary of S maps to r(u,v0)
r(u,v) = < x(u,v), x(u,v) > is the position vector of the image of the point (u,v)
The image of S under T is not a parallelogram - but can be approximated by a parallelogram spanned by the vectors a and b

3. The image of S under T is not a parallelogram - but can be approximated by a parallelogram spanned by the vectors a and b

4. Area

5. Jacobian

6. Polar Coordinates

7. Polar Coordinates

8. Triple Integrals

9. Spherical

10. Spherical