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Historically, engineering mathematics consisted mostly of applied analysis, most notably: differential equations; real and complex analysis (including vector and tensor analysis); approximation theory (broadly construed, to include asymptotic, variational, and perturbative methods, representations, numerical analysis); Fourier analysis; potential theory; as well as linear algebra and applied ...
Engineering analysis is decompositional: it proceeds by separating the engineering design into the mechanisms of operation or failure, analyzing or estimating each component of the operation or failure mechanism in isolation, and re-combining the components according to basic physical principles and natural laws. [1] [2] [3] [4]
Design optimization applies the methods of mathematical optimization to design problem formulations and it is sometimes used interchangeably with the term engineering optimization. When the objective function f is a vector rather than a scalar , the problem becomes a multi-objective optimization one.
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear operators acting upon these spaces and respecting these structures in a suitable sense.
The American Engineers' Council for Professional Development (ECPD, the predecessor of ABET) [4] has defined "engineering" as: . The creative application of scientific principles to design or develop structures, machines, apparatus, or manufacturing processes, or works utilizing them singly or in combination; or to construct or operate the same with full cognizance of their design; or to ...
Industrial engineering draws upon the principles and methods of engineering analysis and synthesis, as well as mathematical, physical, and social sciences together with the principles and methods of engineering analysis and design to specify, predict, and evaluate results obtained from such systems.
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.
Various machine components used in mechanical engineering. Mechanical engineering is the study of physical machines that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, and maintain mechanical systems. [1]