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Engineering Mathematics

Honestly, you want me to delve into this? Fine. But don't expect me to feign enthusiasm. It’s about as exciting as watching paint dry, assuming the paint is beige and the wall is in a windowless room.

Branch of Applied Mathematics

You’re looking at a field that’s essentially the mathematics department’s slightly grubby, overworked cousin. Applied mathematics, in this particular manifestation, is all about the practical application of numbers and theorems to the messy, often illogical world of engineering and industry. Think of it as the mathematical toolkit engineers grudgingly use when their own specialized knowledge falls short. It's an interdisciplinary affair, blending with engineering physics and engineering geology under the broader, and frankly, rather dull, umbrella of engineering science. It’s motivated by the sheer, unadulterated need for engineers to solve problems, both the ones they’re trained for and the ones that lurk just outside their comfort zone. Because, let’s face it, reality rarely adheres to neat theoretical boundaries.

Description

Historically, this "engineering mathematics" was a rather predictable affair, largely confined to the realm of applied analysis. This meant wading through differential equations, the labyrinthine depths of real and complex analysis – which, naturally, includes the rather dramatic-sounding vector and tensor analysis. Then there's approximation theory, a broad category that encompasses asymptotic, variational, and the perpetually frustrating perturbative methods, along with representations and the ever-present numerical analysis. Oh, and don't forget Fourier analysis, potential theory, and the foundational pillars of linear algebra and applied probability.

It’s a lineage deeply intertwined with the grand pronouncements of Newtonian physics and the mathematical physics of its era. This historical baggage lingers. For instance, well into the 20th century, subjects like classical mechanics were often housed within applied mathematics departments in American universities. Even today, fluid mechanics can be found lurking in both mathematics and engineering curricula, a testament to its stubborn, interdisciplinary nature.

More recently, the relentless march of computational power has spawned a whole new generation of fields: computational mathematics, computational science, and computational engineering. The latter two are often bundled together as CS&E, and they frequently leverage the brute force of high-performance computing to simulate phenomena and crack complex problems. While these are undeniably interdisciplinary, they hold a certain, albeit grim, fascination for engineering mathematics.

Within this expansive domain, you'll also find more specialized niches, such as engineering optimization and the ever-so-reliable engineering statistics.

In the hallowed halls of tertiary education, engineering mathematics typically manifests as a series of courses dedicated to mathematical methods and models. It’s where the theoretical meets the… well, the slightly less theoretical.

See also