MAT235Y1 Study Guide - Midterm Guide: Parametric Surface, Tangent Space, Directional Derivative
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MAT235Y1 Full Course Notes
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Final exam materials: every materials you learned in class. However, the most important topics are in the vector calculus, chapter 16. In order to understand the topics, you should be very well equipped with varieties of techniques; parametrization of curves and surfaces, arc length and surface di erentials, computing areas and volumes, change of variables and chain rules. Calculus, chapter 14 such as directional derivatives, limits, tangent planes and etc. The rest of materials you learned are used as tools to study those main topics. Please read the summary of the course below. Single variable calculus: frequently used integrals: trigonometric integrals such as: 0 sin m d = 0, r sin cos3 d and etc. dx and etc: simple substitutions such as: R cos2 d , r sin3 d , r 2 . R 2x + 3 dx, r x x2 + 1 dx, r. R ln x dx, r x cos x dx, r xex dx and etc.