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Exercise 1. Express the following in the simplest possible terms. Be sure to state what kind of object you get: 1-form, 2-form, etc. a) df for f : R² –→ R with f(x, y) = ry²e*+v + x²y. b) do for ø : TR² → R, with o(v1, v2)(21.72) = e"2v1 + 3x1x2V2. c) df ^ø for f, ø as above. d) d(fø) for ƒ, ø as above.

Exercise 1. Express the following in the simplest possible terms. Be sure to state what kind of object you get: 1-form, 2-form, etc. a) df for f : R² –→ R with f(x, y) = ry²e*+v + x²y. b) do for ø : TR² → R, with o(v1, v2)(21.72) = e"2v1 + 3x1x2V2. c) df ^ø for f, ø as above. d) d(fø) for ƒ, ø as above.

Advanced Engineering Mathematics
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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Exercise 1. Erpress the following in the simplest possible terms. Be sure to state what kind of object you get: 1-form, 2-form, etc. a) df for f : R? →R with f(x, y) = xy?e²+y + x?y. b) do for ø : TR² → R, with o(v1, v2)(21.2) = e*2v1 + 3×1X2V2. c) df ^o for f, ̟ as above. d) d(fø) for f, o as above.
Transcribed Image Text:Exercise 1. Erpress the following in the simplest possible terms. Be sure to state what kind of object you get: 1-form, 2-form, etc. a) df for f : R? →R with f(x, y) = xy?e²+y + x?y. b) do for ø : TR² → R, with o(v1, v2)(21.2) = e*2v1 + 3×1X2V2. c) df ^o for f, ̟ as above. d) d(fø) for f, o as above.
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