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.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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