Multivariable Calculus · 免费预览
参数化流形与定向
k-流形作为积分的一般形状，定向作为参数的排序，以及边相匹配而粘合起来的分片形状。
1. The tower of shapes, one definition
The tower of shapes, one definition
2. Orientation as ordered parameters
Orientation as ordered parameters
3. Gluing pieces with matching sides
Gluing pieces with matching sides
4. Worked orientation on the boundary of a square
Worked orientation on the boundary of a square
5. Orienting by permutation
A surface is parametrized by ordered variables . Which reordering gives the same orientation?
6. The seam check
Two surface patches meet along a seam. What does compatible orientation require along it?
7. Dimension census
Which of the following shapes is a parametrized two-manifold?
8. Boundary of a boundary
A compact two-manifold-with-boundary has a boundary that is itself a closed one-manifold. How many boundary curves does a cylinder surface have? Give the count, as a plain number.
9. Orientation count on a connected orientable surface
A connected orientable surface has how many distinct orientations available? Give the count, as a plain number.