ABSTRACT
In this chapter, we introduce the eigenfunction expansions for solving Sturm-Liouville problems, typically related to heat conduction applications. The objective of this chapter is to establish a methodology for solving heat conduction in shallow geothermal systems that will be addressed in subsequent chapters. We first define the concept of initial and boundary value problems. Then introduce the notion of the eigenfunctions and eigenvalues. After that we give a brief description of Fourier series, Fourier transforms and Fourier integrals. Later, examples describing the solution of heat conduction in finite, semi-infinite and infinite media will be presented.
