If you could work number 2 I w For the first few problems in this set, let\[ \mathbf{F}_1 = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} \quad \mathbf{F}_2 = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} \quad \mathbf{F}_3 = \begin{pmatrix} x^2 \\ y^2 \\ z^2 \end{pmatrix} \quad \mathbf{F}_4 = \begin{pmatrix} x \\ 0 \\ 0 \end{pmatrix} \quad \mathbf{F}_5 = \begin{pmatrix} y \\ -x \\ 0 \end{pmatrix} \]1. Let \( S \) denote the unit sphere\[ \mathbf{T}(u, v) = \begin{pmatrix} \cos u \sin v \\ \sin u \sin v \\ \cos v \end{pmatrix}, \quad 0 \leq u \leq 2\pi, \quad 0 \leq v \leq \pi \]and compute(a) \(\iint_{S} \mathbf{F}_1 \cdot d\vec{S}\)(b) \(\iint_{S} \mathbf{F}_2 \cdot d\vec{S}\)(c) \(\iint_{S} \mathbf{F}_3 \cdot d\vec{S}\)(d) \(\iint_{S} \mathbf{F}_4 \cdot d\vec{S}\)(e) \(\iint_{S} \mathbf{F}_5 \cdot d\vec{S}\)2. Let \( S \) denote the square with corners \((1, 1, 1), (-1, 1, 1), (1, -1, 1),\) and \((-1, -1, 1)\), oriented so that the top of \( S \) points in the direction of the positive Z-axis, and compute(a) \(\iint_{S} \mathbf{F}_1 \cdot d\vec{S}\)(b) \(\iint_{S} \mathbf{F}_2 \cdot d\vec{S}\)(c) \(\

The given vectors are .Given S is a square with corners oriented so that the top of S points in the…

For the first few problems in this set, let *-0 -0 - -) -- F₁ = F₂ F3 y² F₁ = F5 = 22 1. Let S denote the unit sphere cos u sin v sin u sin v COS U T(u, v) = and compute (a) fs F₁ ds (b) ff F2 ds . (c) ff F3 d5 (d) ffs F4 d5 (e) ffs F5-ds 3 (a) ff F₁ d5 . (b) ff F2 ds (c) ff F3 d5 . (d) ffs F₁-dS (e) fs F5-dS . 0 < u < 2π, 050 Σπ Y -X 0 2. Let S denote the square with corners (1, 1, 1), (-1, 1, 1), (1,-1, 1), and (-1,-1, 1), oriented so that the top of S points in the direction of the positive Z-axis, and compute

For the first few problems in this set, let *-0 -0 - -) -- F₁ = F₂ F3 y² F₁ = F5 = 22 1. Let S denote the unit sphere cos u sin v sin u sin v COS U T(u, v) = and compute (a) fs F₁ ds (b) ff F2 ds . (c) ff F3 d5 (d) ffs F4 d5 (e) ffs F5-ds 3 (a) ff F₁ d5 . (b) ff F2 ds (c) ff F3 d5 . (d) ffs F₁-dS (e) fs F5-dS . 0 < u < 2π, 050 Σπ Y -X 0 2. Let S denote the square with corners (1, 1, 1), (-1, 1, 1), (1,-1, 1), and (-1,-1, 1), oriented so that the top of S points in the direction of the positive Z-axis, and compute

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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