For minimal attention to modeling in your course, use part of one lecture to touch the highlights of the derivation and analysis in chapter 1 of the rock model, v' = -g. Then follow the presentation in section 1.3 to use that simple example to motivate the elementary analytical, numerical, and graphical concepts to come.
Derive one of the population models, say P' = kP' from section 2.1. Depend upon plausibility arguments and homework assignments like exercises 20 and 21, p. 79-80, of the chapter 2 chapter exercises for the emigration (subsection 2.2.1), logistic (subsection 2.2.2), and heat-flow equations (section 2.3).
Devote your other in-class derivation to the undamped spring-mass
equation without forcing, m x'' + k x = 0 (section 5.1). Leave
the linear and nonlinear pendulum equations (
, etc.) to assigned reading of section 5.2.
Section 5.3, RLC Circuit (equations), and the subsequent analyses of these equations in subsections 6.5.3 (without forcing) and 6.7.2 (with forcing) can be omitted entirely.
Diffusion (section 9.1) is really too subtle to explore without a derivation in class, but the reality of life late in the semester of a minimal-modeling course is that you are likely to cover boundary-value problems fairly quickly. Introduce the boundary-value problems developed in examples 1 and 2, p. 432-433, in class and argue that the types of behavior they can support (e.g., a linear diffusion profile or circular symmetry) are reasonable.
The heat equation (section 9.4) ought to be derived in class if you are going to spend time developing the Fourier machinery of section 9.5 or the finite difference tools of section 9.6. The depth of coverage will depend upon your schedule and your students.