Engineering mathematics is a branch of

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

concerning mathematical methods and techniques that are typically used in

engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...

and

industry Industry may refer to: Economics * Industry (economics), a generally categorized branch of economic activity * Industry (manufacturing), a specific branch of economic activity, typically in factories with machinery * The wider industrial sector ...

. Along with fields like

engineering physics Engineering physics, or engineering science, refers to the study of the combined disciplines of physics, mathematics, chemistry, biology, and engineering, particularly computer, nuclear, electrical, electronic, aerospace, materials or mechanical en ...

and

engineering geology Engineering geology is the application of geology to engineering study for the purpose of assuring that the geological factors regarding the location, design, construction, operation and maintenance of engineering works are recognized and accou ...

, both of which may belong in the wider category

engineering science Engineering physics, or engineering science, refers to the study of the combined disciplines of physics, mathematics, chemistry, biology, and engineering, particularly computer, nuclear, electrical, electronic, aerospace, materials or mechanical en ...

, 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 other fields like sociology, anthropology, psychology, ec ...

subject motivated by engineers' needs both for

practical Pragmatism is a philosophical tradition that considers words and thought as tools and instruments for prediction, problem solving, and action, and rejects the idea that the function of thought is to describe, represent, or mirror reality. ...

theoretical A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be s ...

and other considerations outwith 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 In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

;

real Real may refer to: Currencies * Brazilian real (R$) * Central American Republic real * Mexican real * Portuguese real * Spanish real * Spanish colonial real Music Albums * ''Real'' (L'Arc-en-Ciel album) (2000) * ''Real'' (Bright album) (2010) ...

and

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

(including

vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...

and

tensor analysis In mathematics and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold). Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis ...

);

approximation theory In mathematics, approximation theory is concerned with how function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characteri ...

(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 tends to infinity. In projective geometry and related contexts, ...

, variational, and perturbative methods,

representation Representation may refer to: Law and politics *Representation (politics), political activities undertaken by elected representatives, as well as other theories ** Representative democracy, type of democracy in which elected officials represent a ...

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 In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Josep ...

;

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 two fundamental forces of nature known at the time, namely gravi ...

; 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 matrices. ...

and applied

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

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

Newtonian physics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mech ...

, and the

mathematical physics Mathematical physics refers to 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 t ...

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

classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...

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 plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and bio ...

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 mathematics is an area of mathematics devoted to the interaction between mathematics and computer computation.National Science Foundation, Division of Mathematical ScienceProgram description PD 06-888 Computational Mathematics 2006 ...

computational science Computational science, also known as scientific computing or scientific computation (SC), is a field in mathematics that uses advanced computing capabilities to understand and solve complex problems. It is an area of science that spans many disc ...

, and

computational engineering Computational science and engineering (CSE) is a relatively new discipline that deals with the development and application of computational models and simulations, often coupled with high-performance computing, to solve complex physical problems ...

(the last two are sometimes lumped together and abbreviated as CS&E), which occasionally use

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

for the

simulation A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of Conceptual model, models; the model represents the key characteristics or behaviors of the selected system or proc ...

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 Engineering optimization is the subject which uses optimization techniques to achieve design goals in engineering. It is sometimes referred to as design optimization. Topics * structural design (including pressure vessel design and welded beam ...

and

engineering statistics Engineering statistics combines engineering and statistics using scientific methods for analyzing data. Engineering statistics involves data concerning manufacturing processes such as: component dimensions, tolerances, type of material, and fabric ...

. Engineering mathematics in

tertiary education Tertiary education, also referred to as third-level, third-stage or post-secondary education, is the educational level following the completion of secondary education. The World Bank, for example, defines tertiary education as including univers ...

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

References

{{Engineering fields Applied mathematics

Description

See also

References