lecture7-09[1]

lecture7-09[1] - Math 18.02 (Spring 2009): Lecture 7...

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Unformatted text preview: Math 18.02 (Spring 2009): Lecture 7 Partial derivatives. Tangent plane approximation. February 20 Today: Partial derivatives. Tangent plane approximation. Last time: Velocity & acceleration. Derivatives of · and × product. Kepler’s second law. Reading Material: From Simmos 19.2, 19.3 and 19.4. From the Lecture Notes TA. 2 Partial Derivatives We first recall the concept of derivative for a function: Given a scalar valued function y = f ( x ) we denote the derivative of f at x as f ( x ) = d dx f ( x ) = dy dx x = rate of change of y when one changes x at x = slope of tangent line to curve at the point ( x , f ( x )) 1 On the xy-plane the equation of the tangent line to the graph of y = f ( x ) (curve) at the point P = ( x , y ) where y = f ( x ) is ( y- y ) | {z } ( deviat. of y from y ) = dy dx x ( x- x ) | {z } ( deviat. of x from x ) Partial derivatives: Given a two variable function z = f ( x, y ) we define • the partial derivative of f with respect to x ∂z ∂x = dz dx but hold y (the other variable) constant. = rate of change of z when one changes only x • the partial derivative of f with respect to y ∂z ∂y = dz dy but hold x (the other variable) constant....
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This note was uploaded on 03/01/2009 for the course 18 18.02 taught by Professor Auroux during the Spring '08 term at MIT.

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lecture7-09[1] - Math 18.02 (Spring 2009): Lecture 7...

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