2. (a) Using contours, sketch by hand (not by computer or IT tools) the scalar field f(r)x + y² in the (x, y)-plane. Sketch and label enough contours to make the field clear.(b) Using arrows, thoroughly sketch by hand the vector field u(r) = (x+y+z, yz+x, xyz)in the (x, y)-plane. Pay careful attention to the vectors on the line y = −x.

(a) Sketching the scalar field.The scalar function is given by,f(r)=x+y2Represents a family of…

Answered: 2. (a) Using contours, sketch by hand…

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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Similar questions

F = (x² - y)i + + (4z)j + (x²)k Find the curl (curl calculation) of the vector field?
Show that V² (v-x) = 2V.v+x-V²v, where v is a vector field and x is the position vector of a point in a 3D space.
A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)
(b) Using arrows, clearly sketch the vector field u(r) = (y², x + y, 0) in the (x, y)-plane.
The figure shows the vector field F (x,y) = {2xy,x2 } and three curves that start at (1,2) and end at (3,2). (a) Explain why∫c F. dr has the same value for all the three curves. (b) What is this common value?
Sketch and describe the vector field F (x, y) = (-y,2x)
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Plot the vector field F = (y,sinx) using the viewing window (-2pi,2pi)x(-2pi,2pi).
(b) In the (x, y)-plane, sketch the vector fields v = (y, 2y, 0) and w = (x−y, x+y, 0), clearly labelling which sketch is for which field. (c) For the vector fields defined in part (b), evaluate separately each term in the iden- tity given in part (a) and hence verify the identity in this case. (d) The vector field F has the form F(r) g(r)a, where g(r) is an arbitrary differentiable scalar field and a is a constant vector. Use index notation to express curl F in terms of grad g. Hence, by applying Stokes's theorem to the field F, show that g dr - 1/791 Vg x dS, == with S a smooth open orientable surface bounded by the simple closed curve C. You may assume the scalar triple product rule b × c·d=b∙c×d if vectors b, c and d are not operators.
A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v = (x-y, z + y + 3, z²) and the net is decribed by the equation y = √1-x²-2², y ≥ 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)
Explain how to compute the curl of the vector field F = ⟨ƒ, g, h⟩.
Sketch the vector field. F(2, y) = (-2 2. * y 2 0 2 -2 0 -2 2 -2 2 -2 -2 2 -2 4- -4 -3 -2 -1 2 3 -3- -4+ Clear All Draw: 2.

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