- Section 5.2: What is a diff eq? Provides an example and two solution methods before defining diff eq (and doesn’t define a solution…). Then presents separation of variables via an example. Then a falling body example and an escape velocity example.
- Section 7.5: exponential growth and decay. They motivate y’ = ky via population growth, then solve by separation. Example 1: doubling time. Example 2: growth time. Example 3: radioactive decay. Example 4 and 5: compound interest.
- Extra note: in section 3.10 they present little-o notation.
- Chapter 18: differential equations. Section 18.1: linear first order equations. They define “differential equations”, “ordinary differential equation of order n”, “solution”, “general solution”, “particular solution”, “linear”. They introduce the method of integrating factors, and apply to a mixture problem, to a circuit, and to a battery.
- Section 18.2: second order homogeneous equations. They define “independent” for solutions, the auxiliary equation, and use it to provide a solution to a diff eq with constant coefficients. They don’t intro Euler’s formula but assume it in the complex roots example. Then on to higher order equations.
- Section 18.3: the nonhomogeneous equation. they provide general / particular solution info, do the method of undetermined coefficients, and variation of parameters.
- Section 18.4: Applications of second order equations. A vibrating spring, simple harmonic motion, damping, overdamped, critically damped. Electric circuits.
- This text goes through a laundry-list of methods. Perhaps not so much motivation.