Differential Equations Demystified by Krantz
From Intelligent Perception
Ch. 1. What is a differential equation?
Too many methods?
Ch. 2. Second-order equations.
The main example is about the spring.
Ch. 3. Power series solutions and special functions.
Ch. 4. Fourier series: basic concepts.
I don't see this stuff applied to solving differential equations in this chapter...
Ch. 6. Laplace transforms.
Ch. 7. Numerical methods.
Very short -- Euler method -- but sufficient for this course.
Ch. 8. Systems of first-order equations.
Maybe more physics here would help?