9.2 The Directional Derivative

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9.2 The Directional Derivative

1. gradients
2. Gradient at a point
3. Vector differential operator

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REVVectors in 2D 3D
length
Unit vector
Dot product
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Gradient
del f grad f
Example1 gradients Comput
for
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Gradient at a point
Example2 If find
at (2,-1,4)
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Vector Differential Operator
2D
3D
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Directional Derivative.
Example3 Find the directional derivative of .
at (1,1) in the direction of (A) the unit
vector (B) a unit vector in the direction of
3i4j .(C) a unit vector whose angle with the
positive x-axis is (D) The unit vector 0ij
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Directional Derivative.
Geometric representation (1D)
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Generalization of Partial Diff
In this section we will introduce a type of
derivative, called a directional derivative.
    Suppose that we wish to find the
directional derivative of f at (x0,y0) in the
direction of an arbitrary unit vector u lta,bgt
To do this we consider the surface S with
equation zf(x,y) And we let z0f(x0,y0) then
the point P(x0,y0,z0) lies on S. The vertical
plane that passes though P in the direction of
u intersects S in a curve C. The slope of the
tangent line T to C at P is the directional
derivative of f at (x0,y0) in the direction of u
See this
See this link
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Directional Derivative.
Example5 Find the directional derivative of .
at (1,-1,2) in the direction of
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Directional Derivative.
ezsurf('4x2y2',0,4)
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Example4
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