MATH-M 312 Study Guide - Midterm Guide: Helicoid, Arc Length, Density
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Free response (choose 3 over 2 days: 2 questions: path/line integrals will be main focus of question. Arc length, average values: 2 questions: scalar/vector su(cid:396)fa(cid:272)e i(cid:374)teg(cid:396)als (cid:862) (cid:863) Know definitions and how to compute given parameterizations. Surface area, average values: 1 question: parameterize a surface. Will be somewhat more difficult than implied parameterization needed for integral problems: 1 question: prove a basic property of vector fields involving divergence, gradient, or curl. Things to know: remember change of variables- not tested heavily, but might be needed to complete evaluation of an integral, be familiar with (know how to parameterize and what integrals look like) these curves and surfaces: Surfaces- spheres (be able to immediately know integral/magnitude of normal vector): basic definitions. Can orient all curves, not all surfaces. Curves- more likely to be given difficult-looking parameterizations to compute integrals with. Ci(cid:396)(cid:272)les, ellipses, li(cid:374)es, li(cid:374)e seg(cid:373)e(cid:374)ts, heli(cid:454)es; (cid:271)e p(cid:396)epa(cid:396)ed fo(cid:396) (cid:862)(cid:449)ei(cid:396)de(cid:396)(cid:863) (cid:272)u(cid:396)(cid:448)es.
