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From Wikipedia: "A software engineer is a person who applies the engineering design process to design, develop, maintain, test, and evaluate computer software."

"The engineering design process, also known as the engineering method, is a common series of steps that engineers use in creating functional products and processes. The process is highly iterative - parts of the process often need to be repeated many times before another can be entered - though the part(s) that get iterated and the number of such cycles in any given project may vary.

It is a decision making process (often iterative) in which the basic sciences, mathematics, and engineering sciences are applied to convert resources optimally to meet a stated objective. Among the fundamental elements of the design process are the establishment of objectives and criteria, synthesis, analysis, construction, testing and evaluation.[1]"

It is not dependent on the problem domain, rather on how the work is performed.