LEARNING RESULTS - Recognize and classify a singular or regular problem. - Understand and use the concepts of distinguished limit, dominant balance and scaling. - Understand and use elementary methods to approximate integrals. - Understand and use boundary layer and matched asymptotic expansion methods for ODEs. - Use métodos de escalas múltiples for linear and nonlinear oscillator problems. - Understand and use the Chapman-Enskog method.

- Basic notione of asymptotic analysis. - Approximation of integrals. - Solvability condition for a non-homogeneous linear problem. - Eigenvalue problems. - Poincaré-Linstedt method. - Scaling of singular perturbation problems. - Boundary layer and asymptotic matching. - Method of matched asymptotic expansions. - Method of multiple scales. - Chapman-Enskog method. - Realistic examples in science and engineering