#983 overall
18.303 Linear Partial Differential Equations: Analysis and Numerics
MIT OpenCourseWare
1 recommender · 1 thread · recommended in 1 year, 2019 · score 0.7
An MIT OpenCourseWare graduate course on linear partial differential equations covering both analytical theory and numerical methods, taught by Steven Johnson with course materials using Julia.
One commenter recommends it as the starting point for numerical PDE work and says they highly recommend the Julia-based materials.
Mathematicsadvancedfreevideo lectures#partial differential equations#numerical methods#julia#finite elements#steven johnson
Recommendations by year
20062026
Sure! If you already have a good math background, essentially the only thing left is to do a "bit" of numerical computing. Steven Johnson at MIT has a good course starting this (with Julia! Which is awesome and I highly recommend) [0] and, for further information, it's worth looking at some books (of which there are plenty, as far as I can tell. I studied out of Chew's Waves and Fields in Inhomogeneous Media, but this book is quite out of date and not particularly pedagogically good).
Overall, the mathematics itself is not difficult (essentially, everyone is using some simple preconditioned CG method for solving the linear problems, along with some [sometimes smart, sometimes not] meshing), but generating robust solvers is, almost universally, still an open problem. Depending on what you'd like to simulate and such, you're going to have to make use of the different properties of the operators you're working with to get really good results. We can email and I can say a little more given more details of your project/potentially guide you in a slightly better direction.
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[0] https://github.com/mitmath/18303/tree/fall16