Engineering mathematics: Difference between revisions

Content deleted Content added

Inline

Latest revision as of 21:33, 12 June 2024

Mathematical engineering (or engineering mathematics) is a branch of applied mathematics, concerning mathematical methods and techniques that are typically used in engineering 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 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 (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 probability, outside of analysis. These areas of mathematics were intimately tied to the development of Newtonian physics, and the mathematical physics of that period. This history also left a legacy: until the early 20th century subjects such as classical mechanics were often taught in applied mathematics departments at American universities, and fluid mechanics may still be taught in (applied) mathematics as well as engineering departments.^[1]

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 for the simulation 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.^[2]

Specialized branches include engineering optimization and engineering statistics.

Engineering mathematics in tertiary education typically consists of mathematical methods and models courses.^[3]

References

^ Stolz, Michael (2002), "The history of applied mathematics and the history of society", Synthese, 133 (1): 43–57, doi:10.1023/A:1020823608217, S2CID 34271623
^ T.J. Fairclough, Engineering Mathematics and Computer Algebra.
^ Minimum Courses in Engineering Mathematics, S. Epsteen.

[Stolz2002-1] Stolz, Michael (2002), "The history of applied mathematics and the history of society", Synthese, 133 (1): 43–57, doi:10.1023/A:1020823608217, S2CID 34271623

[2] T.J. Fairclough, Engineering Mathematics and Computer Algebra.

[3] Minimum Courses in Engineering Mathematics, S. Epsteen.

[1]

[2]

[3]

@@ Line 1: / Line 1: @@
+{{Short description|Branch of applied mathematics}}
-'''Engineering mathematics''' is a branch of [[applied mathematics]] that concerns itself with [[mathematical models|mathematical methods and techniques]] that are typically used in [[engineering]] and [[manufacturing|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]] subject motivated by engineers' needs both for [[practical]], [[theoretical]] and other considerations outwith their specialization, and to deal with constraints to be effective in their work.
+{{for|the textbook|Ken Stroud}}
+'''Mathematical engineering''' (or '''engineering mathematics''') is a branch of [[applied mathematics]], concerning [[mathematical models|mathematical methods and techniques]] that are typically used in [[engineering]] and [[manufacturing|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]] 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 principally of [[Mathematical analysis|applied analysis]], most notably: [[differential equations]]; [[real analysis|real]] and [[complex analysis]] (including [[vector analysis|vector]] and [[tensor analysis]]); [[approximation theory]] (broadly construed, to include  [[asymptotic analysis|asymptotic]], [[Calculus of variations|variational]], and [[perturbation theory|perturbative methods]], [[Representation (mathematics)|representation]]s, [[numerical analysis]]); [[Fourier analysis]]; as well as [[linear algebra]] and applied [[probability]].  These areas of mathematics were intimately tied to the development of [[Newtonian physics]].  This history left a legacy as well: until the early 20th century subjects such as [[classical mechanics]] were often taught in applied mathematics departments at American universities, and [[fluid mechanics]] may still be taught in (applied) mathematics  as well as engineering departments.<ref name=Stolz2002>{{Citation
+Historically, engineering mathematics consisted mostly of [[Mathematical analysis|applied analysis]], most notably: [[differential equations]]; [[real analysis|real]] and [[complex analysis]] (including [[vector analysis|vector]] and [[tensor analysis]]); [[approximation theory]] (broadly construed, to include [[asymptotic analysis|asymptotic]], [[Calculus of variations|variational]], and [[perturbation theory|perturbative methods]], [[Representation (mathematics)|representation]]s, [[numerical analysis]]); [[Fourier analysis]]; [[potential theory]]; as well as [[linear algebra]] and applied [[probability]], outside of analysis.  These areas of mathematics were intimately tied to the development of [[Newtonian physics]], and the [[mathematical physics]] of that period.  This history also left a legacy: until the early 20th century subjects such as [[classical mechanics]] were often taught in applied mathematics departments at American universities, and [[fluid mechanics]] may still be taught in (applied) mathematics as well as engineering departments.<ref name=Stolz2002>{{Citation
- | title = The History Of Applied Mathematics And The History Of Society
+ | title = The history of applied mathematics and the history of society
- | url = http://www.springerlink.com/index/T152575218M865W4.pdf
  | year = 2002
  | author = Stolz, Michael
@@ Line 11: / Line 12: @@
  | volume = 133
  | issue = 1
- | accessdate = 2009-07-07
  | doi = 10.1023/A:1020823608217
+| s2cid = 34271623
-}}</ref> Specialized branches include [[engineering optimization]] and [[engineering statistics]].
+ }}</ref>
-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]] for the [[simulation]] 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.
+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]] for the [[simulation]] 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.<ref>T.J. Fairclough, [http://mathapps.net/compalg/compalg.pdf Engineering Mathematics and Computer Algebra.]</ref>
-==Education==
+Specialized branches include [[engineering optimization]] and [[engineering statistics]].
-Engineering mathematics at university level typically consists of mathematical methods and models courses, and books on the topic are extremely popular. In the English-speaking world, "Engineering mathematics" (or some variant thereof)is the name of several bestselling textbooks on the subject. In 2013, a search for books containing the phrase 'engineering mathematics' on [[amazon.com]] and Google Books, produced more than 192,729 and  252,000 items respectively.<ref>[http://www.google.co.uk/search?q=enginering+mathemtcs&btnG=Search+Books&tbm=bks&tbo=1#tbm=bks&sclient=psy-ab&q=engineering+mathematics&oq=engineering+mathematics&gs_l=serp.12...0.0.0.20158.0.0.0.0.0.0.0.0..0.0...0.0...1c..12.psy-ab.0uhyJlaVjT4&pbx=1&bav=on.2,or.r_qf.&bvm=bv.46471029,d.d2k&fp=d09e9696d9397ddb&biw=1366&bih=593 Google Books search for "engineering mathematics"]. Recovered 14 May 2013. </ref><ref>[http://www.amazon.com/gp/search/ref=a9_asi_1?rh=i%3Astripbooks%2Cn%3A283155%2Ck%3Aengineering+mathematics&keywords=engineering+mathematics&ie=UTF8&qid=1368571194#/ref=sr_pg_1?rh=n%3A283155%2Ck%3Aengineering+mathematics&keywords=engineering+mathematics&ie=UTF8&qid=1368571249 Amazon book search for "engineering mathematics"]. Recovered 14 May 2013. ''Disclaimer: this search may contain some irrelevant results.'' </ref> However there is some dissension to this viewpoint as whether or not this is all that constitutes the subject.<ref>Imagining Archimedes blog: [http://imaginingarchimedes.blogspot.co.uk/2012/08/wht-engineering-mathematics-is-not.html Why Engineering Mathematics is not a "service" subject]. Saturday, August 11, 2012. Recovered 14 May 2013. </ref>
+Engineering mathematics in [[tertiary education]] typically consists of mathematical methods and models courses.<ref>[https://www.jstor.org/stable/2974079 Minimum Courses in Engineering Mathematics], S. Epsteen.</ref>
 ==See also==
+{{portal|Engineering|Mathematics}}
-* [[Applied mathematics]]
-*[[Techno-mathematics|Techno-]] and [[industrial mathematics]], similar fields
+* [[Industrial mathematics]]
 * [[Control theory]], a mathematical discipline concerned with engineering
-*[[Further mathematics]]
+* [[Further mathematics]] and [[additional mathematics]], [[A-level]] mathematics courses with similar content
-*[[Mathematical methods in electronics]], [[Signal_processing#Mathematical_methods_applied_in_signal_processing|signal processing]] and [[mathematics of radio engineering|radio engineering]]
+* [[Mathematical methods in electronics]], [[Signal processing#Mathematical methods applied in signal processing|signal processing]] and [[mathematics of radio engineering|radio engineering]]
 ==References==
 <references/>
-* [http://www.whatuni.com/degrees/courses/Degree-list/Engineering-Mathematics-Degree-courses-UK/qualification/M/search_category/8850/loc.html Engineering Mathematics Degree Courses UK;] list of engineering mathematics courses in the United Kingdom. Whatuni.com website, accessed 9 Dec 2012.
-==External links==
-* [http://www.enm.bris.ac.uk/ Dept. of Engineering Mathematics] at [[Bristol University]].
+{{Engineering fields}}
 [[Category:Applied mathematics]]