ABSTRACT
The finite element method (FEM) formulation for solving simple partial differential equations (PDEs) results in the matrix form algebraic equations at the elementary and global levels. This chapter discusses a general form PDE and its matrix equation. It reviews the two relevant concepts, eigenvalues and eigenvectors. Eigenvalues are a special set of scalars that are associated with a matrix equation, and they are sometimes known as characteristic values. Similarly, eigenvectors are a special set of vectors associated with a matrix equation, and they are sometimes referred to as characteristic vectors. The chapter also describes how to solve PDEs with time-dependent terms.
