Lecture08_Gradient_9-5_and_9-6 - The Gradient and...

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1 The Gradient and Applications ± This unit is based on Sections 9.5 and 9.6 , Chapter 9. ± All assigned readings and exercises are from the textbook ± Objectives : Make certain that you can define, and use in context, the terms, concepts and formulas listed below: 1. find the gradient vector at a given point of a function. 2. understand the physical interpretation of the gradient. 3. find a multi-variable function, given its gradient 4. find a unit vector in the direction in which the rate of change is greatest and least, given a function and a point on the function. 5. the rate of change of a function in the direction of a vector. 6. find normal vector and tangent vectors to a curve 7. write equations for the tangent line and the normal line. 8. find an equation for the tangent plane to a surface ± Reading : Read Section 9.5, pages 474-482. ± Exercises : Complete problems 9.5 and 9.6 ± Prerequisites : Before starting this Section you should . . . 9 familiar with the concept of partial differentiation 9 be familiar with vector functions
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Directional Derivatives: definition ± We are interested in how T changes from one point to another. T =20 T =25 T =15 A B ± Consider the temperature T at various points of a heated metal plate. ± Some contours for
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Lecture08_Gradient_9-5_and_9-6 - The Gradient and...

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