MATH 6A Lecture Notes - Lecture 11: Chain Rule, General Idea, Unit Circle
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This is an example of a more general idea. Notice: when we computed , what we really computed was. If is a function in and can be expressed in terms of via a change of variables (essentially a function. Then , and the same for is a 3 by 3 matrix, is a 1 by 3 matrix, and is a 1 by 3 matrix. Exercise: multiply out for yourself to see how the two ideas match up. Recall the parametric description of a line in is is a position vector, Think of this as a vector-valued function . Definition: a path in or is a function (or ) The image of is called a curve in (or ) Is also known as the parametrization or parametric equation of the curve. We also allow the domain to go to infinity, ie this is the unit circle centered on. More generally, is the circle of radius centered on.
