This course is the first part of the lecture series of Finite Element Analysis subject. It takes you through various topics like Matrix Algebra, Differential Equations and their solutions and FEM-Weighted Residue Approach. Various numerical are solved to explain different concepts and their applications. These topics help while solving of next course chapters and also help in understanding of ANSYS solutions. Basic Mathematics is the requirement for understanding of this subject.

We start with Introduction to Finite Element Analysis, its advantages, disadvantages and applications. Then we brush up some basics of Matrix Algebra and learn the Gauss Elimination Method for finding inverse of a higher order matrix.

Further, we move to the Basics of linear differential equations and the ways to calculate their solutions which is called the Exact Method.

Then we study FEM-Weighted Residue Approaches and the 7 methods to find solution of Linear Differential Equations which is a Finite Difference Method based on Taylor's series method and compare the solution with exact method. This is very important as ANSYS solutions need to be checked by exact solution for their accuracy. We study the Weak and Non-Weak form type methods to find the solution namely Sub-domain, Galerkin, Petrov-Galerkin, Collocation, Least Square and Rayleigh Ritz methods.