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| Topic | Zill Chapter(s) | Key sections | |-------|----------------|---------------| | Introduction & definitions | 1 | 1.1 Definitions, 1.2 IVPs | | First-order ODEs | 2 | 2.2 Separable, 2.3 Linear, 2.4 Exact, 2.5 Substitutions | | Applications of 1st order | 3 | 3.1 Growth/decay, 3.2 Cooling, 3.3 Mixtures, 3.4 Circuits | | Higher-order linear ODEs | 4 | 4.1–4.3 Theory, 4.3 Nonhomogeneous (UC & Variation of Parameters) | | Laplace transform | 7 | 7.1 Definition, 7.2 Transforms of derivatives, 7.3 First & second shifting, 7.4 Dirac delta/step functions | | Systems of linear ODEs | 8 | 8.2 Matrix methods, 8.3 Eigenvalues, 8.4 Nonhomogeneous systems | | Numerical methods | 9 | 9.1 Euler, 9.2 Runge-Kutta | | Series solutions | 6 | 6.1 Power series, 6.2 Frobenius |

Note on Chapter 5 (Modeling with higher-order ODEs): Spring/mass, LRC circuits, beams – often skipped but useful for applied exams.

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