Mathematical Techniques in Mechanical Engineering

A graduate-level toolkit course that teaches you to turn mechanical engineering problems — heat conduction, vibrations, elasticity, flow — into differential equations and then actually solve them, rather than just admiring them on a slide. You'll work through five problem sets and three written exams covering linear algebra, ODEs (including Laplace transforms, Frobenius, Bessel, Legendre), and the classical PDEs of mathematical physics via separation of variables and transform methods, mostly out of Kreyszig. It's the analytical backbone for the rest of your MS coursework: continuum mechanics, heat transfer, and vibrations all assume you can already manipulate these objects fluently, so the goal here is fluency, not first exposure.