TITLE: Math Subjects that are prerequisites to Finite Element Method
QUESTION [7 upvotes]: I want to Learn Finite Element Method. What are the Math Subjects that are prerequisite to FEM?
I am a mechanical engineer. FEM was not taught to us in College. :(
I am profficient in Engineering Mechanics, Differential Calculus, Integral Calculus and Basics of Differential Eequations. I also know Matrix manipulations. I understand Fourier Series, Fast Fourier Transform and Basic of Laplace Transform. In the past I have knowledge in Runge-Kutta, Stokes Theorem, Gradient, Divergence and Curl. I can derive the Navier-Stokes Equation.
What other math subject do I need to learn before I study Finite Element Method? Can you suggest online course for FEM (other than MIT OCW)?
Thank you very much.
Joseph

REPLY [6 votes]: Courses
The primary classes you are going to want to have include:

Complex Analysis
Differential Equations (both Theory and Numerical variants and several of each)
Partial Differential Equations (both Theory and Numerical variants and several of each)
Numerical Analysis Courses
Some Programming would not hurt
An algorithms and Computational Complexity course would not hurt

Other Recommendations

Peruse the web for notes
Find software that has various implementations and learn to use it
Look in your local college library for books that interest you as well as others on the web
Look at Open Courseware like at MIT, check out the videos and lecture notes
Check out other open courses like http://www3.open.ac.uk/study/postgraduate/course/t884.htm
Check the prerequisites at the school you want to take this at and see where you are in relation to those
MSE Book Recommedations and resources to study PDE from and How to use FEM to solve a PDE

From all of this, you might be better able to gauge where you are and what you are deficient in.