The course aims to provide students with basic mathematical concepts and problem solving methodologies from the field of differential equations and familiarity with the transformations to solve problems related to the object of study.
Study of ordinary differential equations. First order equations: separable variables, linear, complete, Bernoulli, Ricatti, Clairaut, Lagrange. Analytical, graphical and numerical methods of first order solution. Expatriates and non-expatriates. Methods for solving linear CI, homogeneous and non-homogeneous. Expats and non-expats with constant coefficients and methods of resolving them. Systems CI: Definitions, relation between patent systems solutions and higher order differential equations. Solution of second order differential equation with the method of power series. Polynomials Legendre. Functions Bessel. Differential equations with partial derivatives. Series transformations and Fourier. Transformations Laplace. Inverse transform Laplace. Solving ordinary differential equations by transforming Laplace.