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MATH241 Week 7 Notes

by: Colin Fields

MATH241 Week 7 Notes Math 241

Marketplace > University of Maryland > Math > Math 241 > MATH241 Week 7 Notes
Colin Fields

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About this Document

Lecture and Book notes
Calculus 3
Dr. Grillakis
Class Notes
Calculus, gradient, directional derivatives
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This 2 page Class Notes was uploaded by Colin Fields on Monday October 17, 2016. The Class Notes belongs to Math 241 at University of Maryland taught by Dr. Grillakis in Fall 2016. Since its upload, it has received 5 views. For similar materials see Calculus 3 in Math at University of Maryland.


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Date Created: 10/17/16
Calc III Lec Day _ 10/_/16 Ch. 13.5 Directional Derivatives 1. The derivative of a function, f(x,y), in the direction of unit vector u =(a1,a2) is equal to the product of the partial derivatives of f with the components of u a. 2. This can be extended to functions of more variables by the addition of the products of the additional partial derivatives and unit vector components Calc III Lec Day _ 10/_/16 Ch. 13.6 The Gradient 1. The gradient of a function f is defined as the partial derivatives of f multiplied by their corresponding axial unit vector a. 2. The directional derivative can be written as the dot product of the gradient and the directional unit vector a. b. If computed algebraically, the components can be resolved before summation yielding a function for the directional derivative instead of just a magnitude 3. The gradient of a curve is orthogonal to that curve 4. The gradient can be used to construct a plane parallel to the curve at a point by using the gradient as the normal vector


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