Rafael Silva Sasportes

1. First Order Differential Equations
2.Higher Order  Differential Equations
3. The Laplace Tranform
4. Systems of First Order Linear Equations

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.

E-Learning.

Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one final presence-based exam (100%).

Recommended precedences: Elements of Infinitesimal Analysis II and Linear Algebra II.