L24 Math 233 Lecture Notes - Lecture 31: Parallelogram, Nissan L Engine
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Google docs doesn"t allow me to type matrices, so anytime there is a metrix, the. Note: top row will be distinguished from the bottom row with a division sign. Apply to case from previous lecture using 2x2 determinant formula: Note: the notation above is meant to be written with the paragraphs around the entire column. d. Hypothesis: this computes da" if the functions x(u,v) and y(u,v) are continuously differentiable in d". Note: jacobian also refers to the absolute value of the determinant of that matrix. , uv) v ( y = ( 2 v2 2. U (it"s absolute value is the same) is called the jacobian of x, ) V u, ) v ( y x, ) D f (x(u, ), (u, ))4(u v y v. Example: rcos , sin ) r x, ) r, ( ( y = ( So, the jacobian is rcos os in . For f (x, )dxdy y (x(u, ), (u, ))rdrd v y.
