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Hours	Topic
4	Introduction to Differential Equations Definitions and terminology Initial-value problems Differential equations as mathematical models
8	First-Order Differential Equations Solution curves without a solution; direction fields, autonomous first-order differential equations Separation of variables Linear equations Exact equations Solutions by substitutions Numerical methods; Euler's method, numerical solvers
4	Modeling with First-Order Differential Equations Linear models; exponential growth and decay, Newton's law of cooling, mixture problems Non-linear models; logistic growth, chemical reactions Systems of differential equations; radioactive series, mixtures, predator-prey models
14	Higher-Order Differential Equations Linear differential equations; initial-value and boundary-value problems, homogenous equations, non-homogeneous equations Reduction of order Homogenous linear equations with constant coefficients Undetermined coefficients; supposition approach, annihilator approach Variation of parameters Cauchy-Euler equation Solving systems on linear equations using elimination Non-linear differential equations
5	Modeling with Higher-Order Differential Equations Linear models with initial value problems; spring/mass systems with free undamped motion, free damped motion, and driven motion Linear models with boundary value problems Nonlinear models
7	Series Solutions of Linear Equations Review of power series Solutions about ordinary points Solutions about singular points Special functions; Bessel's Equation, Legendre's Equation
10	The Laplace Transform Definition of the Laplace transform Inverse transforms and transforms of derivatives Operational properties of the transform The Dirac Delta function
6	Systems of Linear First-Order Differential Equations Preliminary theory; supposition principle, independence, general solutions Homogenous linear systems; distinct real eigenvalues, repeated eigenvalues, complex eigenvalues Nonhomogeneous linear systems; undetermined coefficients, variation of parameters Matrix exponentials
4	Numerical Solutions of Ordinary Differential Equations Euler's method Improved Euler's method Runga-Kutta methods (RK4)