**6. Conclusion**

In this chapter, we introduced the finite element (FE) method for approximation the solutions to ODEs and PDEs. More specifically, the FE method is presented for first-order initial-value problems for OEDs, second-order boundary-value problems for ODEs, second-order elliptic PDEs, second-order heat and wave equations. The remaining chapters of this textbook are based on the FE method. The derivation of the FE method for other problems is straightforward. In the remaining chapters, the FE method will developed to solve complicated problems in engineering, notably in elasticity and structural mechanics modeling involving elliptic partial differential equations and complicated geometries. For more details, we refer the reader to [1–4, 6–9] and the references therein.

## **Author details**

Mahboub Baccouch Department of Mathematics, University of Nebraska at Omaha, Omaha, NE, USA

\*Address all correspondence to: mbaccouch@unomaha.edu

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
