Modeling with ordinary differential equations (ODEs). First-order ODE solution methods. Second order linear equations. Coefficients method to be determined, parameter variation method. Applications. Existence and uniqueness of solutions. Numerical methods. ODE systems, stability. Solution of linear ODE systems. Matrix exponential. Phase portrait, equilibrium points and stability of linear systems. Nonlinear systems: phase portrait, balance points and stability. Ecological models based on ODEs; predator-prey systems, species competition.
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