Engineering mathematics (also called Mathematical Engineering) 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 outwith their specialization, and to deal with constraints to be effective in their work.
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.
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.
Engineering mathematics at tertiary level typically consists of mathematical methods and models courses, and books on the topic are extremely popular. For example, "Engineering Mathematics: YouTube Workbook"  received over 300,000 downloads in 2012, making it the most popular title on Bookboon.com.
In the English-speaking world, "Engineering mathematics" (or some variant thereof) is the name of several bestselling university 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 457,000 items respectively. However, there is some dissension to this viewpoint as to whether or not this is all that constitutes the subject.
- Applied mathematics
- Techno- and industrial mathematics, similar fields
- Control theory, a mathematical discipline concerned with engineering
- Further mathematics and additional mathematics, A-level mathematics courses with similar content
- Mathematical methods in electronics, signal processing and radio engineering
- Stolz, Michael (2002), "The History Of Applied Mathematics And The History Of Society" (PDF), Synthese 133 (1): 43–57, doi:10.1023/A:1020823608217, retrieved 2009-07-07
- Tisdell, Christopher (2012), Engineering Mathematics: YouTube Workbook, retrieved 2014-02-11
- "Global educator Chris Tisdell: Why free textbooks and videos are the key to future learning". Bookboon's Blog. June 6, 2013. Retrieved February 11, 2014.
- Google Books search for "engineering mathematics". Recovered 14 May 2013.
- Amazon book search for "engineering mathematics". Recovered 29 June 2013. Disclaimer: this search may contain some irrelevant results.
- Imagining Archimedes blog: Why Engineering Mathematics is not a "service" subject. Saturday, August 11, 2012. Recovered 14 May 2013.
- Engineering Mathematics Degree Courses UK; list of engineering mathematics courses in the United Kingdom. Whatuni.com website, accessed 9 Dec 2012.
- Dept. of Engineering Mathematics at Bristol University.
- eFunda:Engineering Mathematics at Engineering Fundamentals
- Industrial and Engineering Mathematics research group at Plymouth University
- Master in Mathematical Engineering at KU Leuven