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I am reading Barrett O'Neil's book: Elementary Differential Geometry ...
I need help with fully understanding the example on wedge products of differential forms in O'Neill's text on page 31 in Section 1.6 ..
The example reads as follows:
I do not follow the computations in this example ... can someone please explain (in very simple terms) how the example "works" ... essentially how do we justify each step in the reasoning ...
Particularly puzzling for me is the following ... ...
... in the first equation (equation *) we find
[itex]d(fg \ dx \ dy ) = \partial (fg) / \partial z \ dz \ dx \ dy [/itex]
How is this step justified?
... then I find all the steps in the second and third equations puzzling as well ...
Can someone explain and justify the steps in the example in terms of O'Neill's Definitions, Theorems and Lemma's ... ...
To give readers of this post the context, notation and necessary Definitions, Theorems and Lemma's, I am providing the text of Section 1.6: Differential Forms ... ... as follows ... ...
I need help with fully understanding the example on wedge products of differential forms in O'Neill's text on page 31 in Section 1.6 ..
The example reads as follows:
I do not follow the computations in this example ... can someone please explain (in very simple terms) how the example "works" ... essentially how do we justify each step in the reasoning ...
Particularly puzzling for me is the following ... ...
... in the first equation (equation *) we find
[itex]d(fg \ dx \ dy ) = \partial (fg) / \partial z \ dz \ dx \ dy [/itex]
How is this step justified?
... then I find all the steps in the second and third equations puzzling as well ...
Can someone explain and justify the steps in the example in terms of O'Neill's Definitions, Theorems and Lemma's ... ...
To give readers of this post the context, notation and necessary Definitions, Theorems and Lemma's, I am providing the text of Section 1.6: Differential Forms ... ... as follows ... ...
Attachments

O'Neill  EXAMPLE on page 31  Wedge Products of Differential Forms.png77 KB · Views: 877

O'Neill  1  Section 1.6  page 28  Differential Forms  PART 1 .png106.3 KB · Views: 837

O'Neill  2  Section 1.6  page 29  Differential Forms  PART 2 .png84.6 KB · Views: 801

O'Neill  3  Section 1.6  page 30  Differential Forms  PART 3 .png75.2 KB · Views: 741

O'Neill  4  Section 1.6  page 31  Differential Forms  PART 4 .png117.8 KB · Views: 863