What is the difference in usage between меняться and изменяться to convey the idea of "change" or "vary"? For example, if someone is talking about a vector field along a curve (that's the context in which this question came up), is there a preferred choice between

(1) касательный вектор меняется гладко от точки к точке


(2) касательный вектор изменяется гладко от точки к точке

or are these absolutely synonymous?


In the meaning of "vary, become different" the verbs are synonymous, with both used in academic style with no difference in connotation — i.e. the choice of a verb in a particular sentence is up to the author (for example, to avoid using only "изменяться" several times in a row).

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