Both Uses

resolution
in
The Story of Edgar Sawtelle
(Edited)

My New Year's resolution.
p. 144.3 *

resolution = firm decision to do something
If he looked into the strobed rain too long, he ended up curled and oblivious, for if there was no figure to be seen in the falling drops of water, he felt abandoned, and if he saw anything—a shape, a movement, a form—he screamed, silently, despite all resolution to the contrary.
p. 353.9 *

resolution = determination (firmness of purpose)

Definitions:

(1) (resolution as in: a New Year's resolution)
a firm decision to do something
(2) (resolution as in: a United Nations resolution)
a formal statement of decision or opinion voted on by a group

While a resolution typically expresses an opinion and has no legal force, when used in early U.S. history or in the expressions joint resolution of Congress or continuing resolution, it becomes a synonym for legislation (meaning that it carries the force of law).
(3) (resolution as in: Her resolution weakened.)
determination (firmness of purpose)
(4) (resolution as in: resolution of the dispute)
a solution or outcome
(5) (meaning too rare to warrant focus)
Much less commonly, other meanings of resolution include:
- a measure of optic detail -- as in: "The photograph has excellent resolution."
- separation into different parts -- as in: "When force is applied to an inclined plane there is resolution of the force into horizontal and vertical components."
- conversion to something else -- as in: "... resolution of the chord from dissonance (an unstable sound) to consonance (a more stable sound)."
- reduction to or conversion to something else -- as in: "It permits resolution of a URL to an IP address."