The Finite Element Method

FEM is the workhorse method for actually solving the PDEs you meet in solid mechanics, heat transfer, and vibrations once geometry or boundary conditions kill any hope of an analytical answer, this course builds it from the ground up, starting with weak forms and weighted residuals, then shape functions, assembly, and error analysis on 1D problems before scaling the same machinery to 2D/3D elliptic, parabolic, hyperbolic, and nonlinear cases. Expect homework sets and a coding component where you implement the discretizations yourself rather than treating a commercial solver as a black box. It assumes you're solid on calculus, linear algebra, and ODEs/PDEs, and it's the bridge between that math background and the simulation tools you'll lean on for research or any serious mechanical/civil/aerospace analysis work afterward.