Mathematical engineering (or engineering mathematics) is a branch of

applied mathematics Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...

, concerning mathematical methods and techniques that are typically used in

engineering Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...

and industry. Along with fields like engineering physics and engineering geology, both of which may belong in the wider category engineering science, engineering mathematics is an

interdisciplinary Interdisciplinarity or interdisciplinary studies involves the combination of multiple academic disciplines into one activity (e.g., a research project). It draws knowledge from several fields such as sociology, anthropology, psychology, economi ...

subject motivated by engineers' needs both for practical, theoretical and other considerations outside their specialization, and to deal with constraints to be effective in their work.

Description

Historically, engineering mathematics consisted mostly of applied analysis, most notably: differential equations; real and

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

(including vector and

tensor analysis In mathematics and physics, a tensor field is a function (mathematics), function assigning a tensor to each point of a region (mathematics), region of a mathematical space (typically a Euclidean space or manifold) or of the physical space. Tens ...

); approximation theory (broadly construed, to include

asymptotic In analytic geometry, an asymptote () of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the ''x'' or ''y'' coordinates Limit of a function#Limits at infinity, tends to infinity. In pro ...

, variational, and perturbative methods, representations,

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

); Fourier analysis;

potential theory In mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" was coined in 19th-century physics when it was realized that the two fundamental forces of nature known at the time, namely g ...

; as well as

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...

and applied

probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...

, outside of analysis. These areas of mathematics were intimately tied to the development of Newtonian physics, and the

mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...

of that period. This history also left a legacy: until the early 20th century subjects such as

classical mechanics Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...

were often taught in applied mathematics departments at American universities, and

fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them. Originally applied to water (hydromechanics), it found applications in a wide range of discipl ...

may still be taught in (applied) mathematics as well as engineering departments. The success of modern numerical computer methods and software has led to the emergence of computational mathematics, computational science, and computational engineering (the last two are sometimes lumped together and abbreviated as CS&E), which occasionally use

high-performance computing High-performance computing (HPC) is the use of supercomputers and computer clusters to solve advanced computation problems. Overview HPC integrates systems administration (including network and security knowledge) and parallel programming into ...

for the

simulation A simulation is an imitative representation of a process or system that could exist in the real world. In this broad sense, simulation can often be used interchangeably with model. Sometimes a clear distinction between the two terms is made, in ...

of phenomena and the solution of problems in the sciences and engineering. These are often considered interdisciplinary fields, but are also of interest to engineering mathematics. Specialized branches include engineering optimization and engineering statistics. Engineering mathematics in

tertiary education Tertiary education (higher education, or post-secondary education) is the educational level following the completion of secondary education. The World Bank defines tertiary education as including universities, colleges, and vocational schools ...

typically consists of mathematical methods and models courses.Minimum Courses in Engineering Mathematics
S. Epsteen.

References

{{Engineering fields Applied mathematics

Description

See also

References