Class Introduction to Ordinary Differencial Equations

Metods of resolving the first ordes ODEs and the second order linear ODEs. Laplace transform and systems of linear ODEs. Relevant for describing various processes in engineering and informatics.

Not applicable

1. Generalities and examples of ODEs 2. First-order ODEs (separable, linear, exact, homogeneous, Bernoulli equation, Riccati equation, applications) 3. Second-order linear ODEs (generalities, Wronskian, homogeneous with constant coefficients, inhomogeneous, variation of parameters) 4. Higher-order linear ODEs 5. Laplace transform (definition and properties, solving ODEs using the Laplace transform) 6. First-order linear ODE systems 7. Stability of ODE solutions  

The students will get the homework assingments, which will help them to better understand a given subject of study.

W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, John Willey & Sons, Inc., 2009 Y. A. Cengel and W. J. Palm III, Equações Diferenciais, McGraw Hill/bookman/AMGH Editora Ltda, 2014 J. E. Villate, Equações Diferenciais e Equações de Diferenças, Universidade do Porto, 2001