Learning to apply the concepts and techniques of Differential Equations in the program in formulating and solving problems of theoretical nature and in mathematical modeling.
1. First Order Differential Equations: Linear Equations; Nonlinear Equations; Modeling with first Order Equations; The Existence and Uniqueness Theorem.
2. Higher Order Differential Equations: Homogeneous Equations with Constant Coefficients; Fundamental Solutions of Linear Homogeneous Equations; Nonhomogeneous Equations; Method of Undetermined Coefficients; Variation of Parameters; Modeling with Higher Order Equations
3. The Laplace Transform: Solution of Initial Value Problems; Differential Equations with Discontinuous Forcing Function.
4. Systems of First Order Linear Equations: Homogeneous Linear Systems; Fundamental Matrices; Nonhomogeneous Linear Systems.
W. E. Boyce & R. C. DiPrima, Equações Diferenciais Elementares e problemas de Valores de Contorno, Rio de Janeiro: Livros Técnicos e Científicos Editora.