Topic outline

  • Overview

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  • Table of Contents

  • Introduction

  • Chapter I: On Integrals

    In this section, we provide a review of double, triple, and curvilinear integrals and their applications through variable transformations. Additionally, we introduce various techniques for calculating integrals using vector analysis theorems, including the Green-Riemann theorem, divergence theorem, and Stokes' theorem.

  • Chapter II: Functional Spaces

    In this chapter, we provide a review of Hilbert spaces, specifically Sobolev spaces, where we aim to address the following points:

    1. Distributional Derivatives.
    2. The Density of D(Ω) in the Sobolev Space.
    3. The Lax-Milgram Theorem.

  • Chapter III: Variational Methods

    This chapter discusses variational techniques, which means transforming an initial value problem or a boundary value problem (referred to as PC or PI, respectively) into a variational problem using the Green's formula. This is denoted as PV (Variational Problem).

  • Chapter IV: Projection Methods

    This chapter is essential for understanding the finite element method, as we require these projection methods, namely the Ritz and Galerkin methods, or sometimes the Ritz-Galerkin method.

  • Chapter V: Introduction to the Finite Element Method

  • References

  • Exams with Solutions

    In this file, you will find past exams from the years 2012-2020 with solutions.