Master of:
- Resolution of elementary ordinary differential equations; resolution of linear differential equations and systems of linear differential equations.
- Existence, uniqueness and continuous dependence of solutions of ordinary differential equations.
- Gauss and Stokes theorems, general properties of the divergence and curl of vector fields, and applications.
- Resolution of elementary linear partial differential equations of 1st and 2nd order.
- General properties and convergence of Fourier series, Fourier transform and applications.
1. Basic concepts: Set of complex numbers; Special functions; Decomposition of rational functions; Exponential of matrices; convolution of functions.
2. Fourier series: Periodic functions and continuity; Orthogonal functions; Fourier series and transform.
3. Laplace Transform: Definition, theorems and properties.
4. Equations and Systems: Ordinary differential equations; Integration factor; Variation formula for constants; Qualitative theory; Linear systems of ordinary differential equations; Applications of the Laplace Transform.
5. Vector calculus: Surfaces in R3; Surface integrals of scalar and vector fields; Gauss and Stokes theorems; Divergence and curl of vector fields; Obtaining the differential equations of continuity, wave, heat, Laplace and Poisson.
6. Partial Differential Equations: Linear partial differential equations; Wave, heat, Laplace's equation and Poisson's equation; Method of separating variables. Applications of the Fourier series and transform.
The course content is taught in theoretical-practical classes, developing some practical examples of application, whenever possible, in the various branches of engineering.
In practical classes, exercises present in the course support books are solved. The exercise sheets in the discipline are only introduced as a reinforcement of the exercises already present in the discipline's bibliography, or in support of practical classes.
At the end of each class, a summary is released by the teacher, which contains suggestions for reading specific to the material taught in the classroom, as well as the location of the suggested exercises in the bibliography.
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