MATH 225: Ordinary Differential Equations

An introduction to the theory and solution methods for ordinary differential equations (ODEs). Topics cover first-order differential equations (separable, linear, exact), second-order linear ODEs with constant coefficients, method of undetermined coefficients, variation of parameters, Laplace transforms, and linear systems of ODEs.

• First-order differential equations: separable equations, integrating factors, exact equations, and Bernoulli models in MATH 225
• Higher-order linear equations: characteristic equations, undetermined coefficients, and variation of parameters
• Laplace transform techniques: operational properties, Dirac delta functions, step functions, and initial value problems
• Systems of differential equations: phase portraits, stability analysis, eigenvalues, and matrix solutions in Ordinary Differential Equations