Differential equations don't ask for a new kind of mathematics — they ask you to redeploy tools you already have, aimed at a new kind of question. Instead of solving for a number, you'll be solving for a function, and every technique this course uses to get there is one you've already practiced somewhere else: antiderivatives and partial fractions from integral calculus, complex numbers and Euler's formula from precalculus and calculus, matrices and eigenvalues from linear algebra, partial derivatives from multivariable calculus, and the convergence machinery of power series from Calculus II.
This chapter doesn't teach any of that again from scratch. It's a quick refresher, pointed at exactly the pieces this course leans on hardest: integration techniques you'll run in reverse, partial fractions you'll need to invert a Laplace transform, complex exponentials that turn oscillation into algebra, matrix eigenvalues that classify an entire system's long-term behavior from four numbers, and the improper integrals and power series that make the Laplace transform and the series-solution method possible at all.
Skim what you already have cold; slow down on whatever feels rusty. By the end of this chapter you'll have every tool laid out on the bench, so the next chapter can start building with them immediately.