MATH 599 Midterm: MATH 5B UCSB 5B Fall 06 5bFRS
Document Summary
Here is a brief list of the key topics we have covered since the rst midterm. You should know how to do each thing listed and/or know the de nitions of the key concepts. The numbers in parantheses refer to the numbering system in the text. These are the most important formulas/facts/de nitions that you should have memorized and understand how to use: ch. 2. 10: partial derivatives of implicit functions: (2. 61), (2. 68: ch. 2. 12: partial derivatives of inverse functions: (2. 79), (2. 82) and the jacobian matrix version of (2. 82) which is stated just above (2. 82), but not numbered: cylindrical and spherical coordinates: (2. 83), (2. 84, ch. 2. 13: tangent vectors (2. 90), tangent lines to curves (2. 92), normal vectors, Gradient (2. 103), tangent planes to surfaces (2. 100: ch. 2. 15, 2. 16, 2. 18: higher order partial derivatives (2. 124), laplacian (2. 125), 2. 19: relative extrema: theorem on p. 151 (2. 146-149), critical points, saddle. Points, extreme value theorem (p. 153: ch.
