Midterm I Study Guide

Midterm I Study Guide - obtained by differentiating f with...

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Calculus III Midterm I Study Guide Chapters 14.1 – 16.4 Chapter 14 – Vector Calculus Tangent Vector Unit Tangent Unit Normal The plane determined by the unit tangent and unit normal is called the osculating plane, given by Arc Length Parametrize a Curve by Arc Length Curvature of a Plane Curve or Chapter 15 – Functions of Several Variables Level Curves Let and identify which quadric surface is made. Plug in arbitrary values for c to plot the level curves. Projections The projection of a curve onto a plane is found by equating the two equations by the variable in the plane in which the curve is being projected. Partial Derivatives The partial derivative of with respect to x is the function

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Unformatted text preview: obtained by differentiating f with respect to x keeping y fixed. This is true for any partial derivative. Open and Closed Sets If greater/less than or equal to closed If greater/less than open If a combination of both neither Limits and Continuity Equality of Mixed Partials For a given mixed partial , take the derivative of the function a by differentiating with respect to b. Hessian Matrix: Chapter 16 – Gradients; Extreme Values; Differentials Gradient Directional Derivatives The Chain Rule The Gradient as a Normal Normal Vector: Perpendicular to Gradient: Tangent Vector: Tangent Lines and Tangent Planes Tangent Line: Normal Line:...
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This note was uploaded on 09/12/2011 for the course MATH 2401 taught by Professor Morley during the Spring '08 term at Georgia Tech.

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Midterm I Study Guide - obtained by differentiating f with...

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