Minimal numerical methods

A minimal treatment of numerical methods would quickly introduce Euler's method (subsection 1.3.4) as part of the survey presented in chapter 1, Prologue. A day devoted to the geometric interpretation of Euler's method (subsection 3.1.1) and a corresponding geometric motivation of Heun's method (subsection 3.1.3) could conclude with a statement of fourth-order Runge-Kutta (subsection 3.1.5). (``Intuitively, RK4 is better because it is averaging slopes at several points along the way from t to $t + \mbox{$\Delta t$}$.'')

The range of exercises supporting initial-value solvers was described previously on p. .

Sections 9.3, Boundary-Value Problems: Numerical Methods, and 9.6, Initial-Boundary-Value Problems, can be omitted entirely without loss of continuity.