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DSWD-RLA Form 1 Republic of the Philippines Department of Social Welfare and Development CHECKLIST OF REQUIREMENTS A. FOR REGISTRATION OF AUXILIARY SWDA 1. New Application Accomplished Application Form Certified true copy of Certificate of Registration and Articles of Incorporation and by-laws SEC for a non-stock non-profit or non-stock profit-oriented-entity CDA for a Cooperative Updated certification on the SWDA s status of operation applicable only if the date of registration with the...
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I'm going to do some lectures on differential forms and from the point of view of we've just finished a standard multivariable basic vector calculus class and we want to know how to do things better and here's some hints that there is a better way to do things at least from the way I run the class some things that we've seen one is that when we have a function f and we take its gradient we think of that as a vector field and so that's assigning to every point in space a column vector F sub X F sub y F sub Z I'm going to do with us all in three dimensions for a while but then we'll switch and see what happens happen to two and then the big payoff is when we go to more than three dimensions later because we know that when we write things as arrows we really should be thinking of those as column vectors we know that from a little bit of linear algebra that we know but the trouble is that's just really the wrong way to put these derivatives together because the right way to put these derivatives together is the matrix of derivatives and since this is a function from R 3 to R then the matrix of derivatives should be exactly the same kind of function just a linear function and that's a row vector F X F Y FC those are just the partials partial F partial X just you know the Savoy to write that without the partial derivative symbol okay so that that might me seem like a minor issue but that's one of the hints that we're kind of thinking about this wrong the defector field seems to suggest to be a column vector and yet the matrix of derivatives which we know is really good because it works with a chain rule really well and believe me that's really significant so that's one hint that we're doing something wrong and a related hint is the geometry of the gradient now you might think while the geometry of the gradient that was one of the coolest things about it but there's a couple of things that are a little bit weird about that okay so for example if I look at f of X Y Z actually you know what I lied let's just go to two dimensions real quick it's going to easier to draw the picture f of X Y is just x squared plus y squared or a standard example I always come back to then if I draw the level sets usually the best picture for that is the level set so here's level set with level one level two is actually at route 2 level 3 is even a little tighter closer to that level 4 these guys are getting closer together as we know that's indicating steeper okay and so the horizontal separation between the levels is getting smaller but what happens to the gradient vector we get bigger the gradient here is 2x 2y okay or again I really should be writing as a column vector if I'm thinking of it as a vector field and that gets bigger so at 1 0 it's a 2 comma 0 but then out here it's actually bigger and it's a little bit odd that the spacing gets smaller when the arrows get bigger it'd be more natural if as the spacing got smaller the arrows got smaller but it seems backwards...