Graphically show the following scalar fields by showing constant contours with field values of f = 0, 1, 2: (a) f(x, y, z)= x+y (b) f(x, y, z)= x² + y² (c) f(x, y, z)= x+y+z (d) f(r, o, z) = r (e) f(r,0,0) =

Graphically show the following scalar fields by showing constant contours with field values of f = 0, 1, 2: (a) f(x, y, z)= x+y (b) f(x, y, z)= x² + y² (c) f(x, y, z)= x+y+z (d) f(r, o, z) = r (e) f(r,0,0) =

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Concept explainers

Gradient of a Scalar Field

Consider a room or a place where the temperature is denoted by a scalar field T, such that at each point (x, y, z), the temperature is given as T(x, y, z). It is independent of time, in which the temperature rises most quickly. The gradient of T will show the direction at that point by moving away from (x, y, z). How far will the rise in temperature in that direction be determined by the gradient magnitude? Consider a surface that has a height above sea level at point (x, y) which is given by H(x, y). At that point, pointing in the direction of the steepest slope or grade is the gradient of H. The magnitude of the gradient of the vector gives the steepness of the slope at that point. How a scalar field changes in another direction can be measured by the gradient by taking a dot product rather than just the direction of the greatest change?

Question

Parts A, B and C

Graphically show the following scalar fields by showing constant contours with field values
of f = 0, 1, 2:
(a) f(x, y, z) = x + y
(b) f(x, y, z)= x² + y²
(c) f(x, y, z)= x+y+z
(d) f(r, o, z)=r
(e) f(r,0,0) =
=
elk
Φ
π

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