Engineering Mathematics is the art of applying mathematics to complex real-world problems. It combines mathematical theory, practical engineering and scientific computing to address today’s technological challenges.
Engineering Mathematics is a creative and exciting discipline, spanning traditional boundaries. Engineering mathematicians can be found in an extraordinarily wide range of careers, from designing next generation Formula One cars to working at the cutting edge of robotics, from running their own business creating new autonomous vehicles to developing innovative indices for leading global financial institutions.
The key skill of an engineering mathematician is mathematical modelling: the art of applying mathematics to complex real-world problems. Problem solving of this kind really is an art that can only be learnt from hands-on experience, so that’s how we teach it: using case studies taken from a whole range of engineering, scientific, industrial and business applications. A thread of mathematical modelling units runs throughout all our degree programmes. In these you will work in teams to tackle challenging and open-ended problems, applying the theory you have learnt in other units.
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 in tertiary education typically consists of mathematical methods and models courses
See Advanced Engineering maths by Alan Jeffery