1. First-order ODEs: basic concepts, ordinary differential equations (ODEs), separable ODEs, modeling, initial value problems, exact ODEs, integrating factors, linear ODEs, Bernoulli equation.
2. Second-order homogeneous linear ODEs: homogeneous linear ODEs, reduction of order, homogeneous ODEs with constant coefficients, Euler-Cauchy equation.
3. Second-order non-homogeneous ODEs: non-homogeneous ODEs, solution by undetermined coefficients, solution by variation of parameters.
4. Higher order non-homogeneous ODEs: homogeneous linear ODEs, non-homogeneous ODEs.
5. Laplace transforms: transform, inverse transform, transforms of derivatives and integrals, ODEs, unit step function, second shifting theorem, Dirac’s delta function, differentiation and integration of transforms, convolution, integral equations, partial fractions, systems of ODEs.