1-8 SCALAR FIELDS IN THE PLANE Let the temperature T' in a body be independent of z, so that it is given by a scalar function T = T(x, t). Identify the isotherms T(x, y) = const. Sketch some of them. 1. T = x² - y2 2. T = xy 3. T = 3x - 4y 4. T = arctan (y/x) 5. T = y/(x² + y²) 6. T = x/(x² + y²) 7. T = 9x² + 4y² 8. CAS PROJECT. Scalar Fields in the Plane. Sketch or graph isotherms of the following fields and describe what they look like. (b) x²y - y³/3 (a) x² - 4x - y² (c) cos x sinh y (e) e sin y (d) sin x sinh y (f) 2x cos 2y (h) x² - 2x - y2 (g) x4 - 6x²y2 + y4 SCALAR FIELDS IN SPACE 9-14 What kind of surfaces are the level surfaces f(x, y, z) = const? 10. f = 9(x² + y²) + z² 9. f= 4x - 3y + 2z 11. f = 5x² + 2y² 13. f=z-(x² + y²) 12. f = z √x² + y2 14. f = x - y²
1-8 SCALAR FIELDS IN THE PLANE Let the temperature T' in a body be independent of z, so that it is given by a scalar function T = T(x, t). Identify the isotherms T(x, y) = const. Sketch some of them. 1. T = x² - y2 2. T = xy 3. T = 3x - 4y 4. T = arctan (y/x) 5. T = y/(x² + y²) 6. T = x/(x² + y²) 7. T = 9x² + 4y² 8. CAS PROJECT. Scalar Fields in the Plane. Sketch or graph isotherms of the following fields and describe what they look like. (b) x²y - y³/3 (a) x² - 4x - y² (c) cos x sinh y (e) e sin y (d) sin x sinh y (f) 2x cos 2y (h) x² - 2x - y2 (g) x4 - 6x²y2 + y4 SCALAR FIELDS IN SPACE 9-14 What kind of surfaces are the level surfaces f(x, y, z) = const? 10. f = 9(x² + y²) + z² 9. f= 4x - 3y + 2z 11. f = 5x² + 2y² 13. f=z-(x² + y²) 12. f = z √x² + y2 14. f = x - y²
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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Please solve Any two questions from here and get the thumbs up please show neat and clean work
Transcribed Image Text:1-8 SCALAR FIELDS IN THE PLANE
Let the temperature T' in a body be independent of z, so that
it is given by a scalar function T = T(x, t). Identify the
isotherms T(x, y) = const. Sketch some of them.
1. T = x² - y2
3. T = 3x - 4y
5. T = y/(x² + y²)
2. T = xy
4. T = arctan (y/x)
6. T = x/(x² + y²)
7. T = 9x² + 4y²
8. CAS PROJECT. Scalar Fields in the Plane. Sketch
or graph isotherms of the following fields and describe
what they look like.
(b) x²y-y²/3
(a) x² - 4x - y²
(c) cos x sinh y
(e) e sin y
(d) sin x sinh y
(f) 2 cos 2y
(g) x46x²y2 + y4
(h) x² - 2x - y2
SCALAR FIELDS IN SPACE
9-14
What kind of surfaces are the level surfaces f(x, y, z) =
const?
9. f= 4x - 3y + 2z
10. f = 9(x² + y²) + z²
√x² + y2
12. f = z
11. f = 5x² + 2y²
13. f=z-(x² + y²)
14. f = x - y²
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