Q.4 Make a chart of all the new nota... [FREE SOLUTION]

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Chapter 14: Q.4 (page 1140)

Make a chart of all the new notation, definitions, and theorems in this section, including what each new thing means in terms you already understand.

Short Answer

Expert verified

Defination covered :

Stokes' Theoram

Curl

Line intergral

Surface intergral

Step by step solution

Step 1. Given

We need to make a chart .

Step 2. Chart.

$All the new notation are as follows : 路 Generalize Green' s theorem to smooth surface other than the plane . 路 Stokes' theoram, 路 {鈭�}_{c} F (x, y, z) . dr, 路鈭� {鈭�}_{s} curl F (x, y, z) . ndS . Chart :$

Notation	Meaning, Definition or Theorems
Stokes' Theoram	Let S be an oriented, smooth or piecewise-smooth surface bounded by a curve C. Suppose that n is an oriented unit normal vector of S and C has a parametrization that traverses C in the counterclockwise direction with respect to n. If a vector field F = F₁颈+贵鈧俲+贵₃k is defined on S, then, ${鈭�}_{c} F (x, y, z) . dr = 鈭� {鈭�}_{s} curl F (x, y, z) . ndS .$
${鈭�}_{c} F (x, y, z) . dr$	Line intergral of vector field.
$鈭� {鈭�}_{s} curl F (x, y, z) . ndS .$	Surface intergral of curl of vector field .

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91影视

Make a chart of all the new notation, definitions, and theorems in this section, including what each new thing means in terms you already understand.

Short Answer

Step by step solution

Step 1. Given

Step 2. Chart.

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