Euler's method is introduced quickly in subsection 1.3.4, part of the survey in chapter 1, Prologue, of some of the major ideas in the text. Euler, Heun (RK2), and fourth-order Runge-Kutta are covered more completely in section 3.1, Numerical Methods. Finite difference methods for (ordinary) boundary-value problems are developed in section 9.3, Boundary-Value Problems: Numerical Methods, and the method of lines for the heat equation in section 9.6, Initial-Boundary-Value Problems: Numerical Methods.
There are two goals in these introductions, developing usable if unsophisticated numerical tools and building mathematical and computational intuition in anticipation of deeper study later in the curriculum. Of course, Euler, Heun, and RK4 are ``baby'' methods, intuitive building blocks for the adaptive initial-value methods available via DELab's access to MATLAB's ode23, ode45, etc. The finite difference method and the method of lines are in a similar category, pedagogic rather than truly practical without more sophisticated enhancements.