Class Differential Equations

In many situations in mathematics and its applications, it is natural to consider models that establish relationships involving not only variables, but also their variations. The equations that contain derivatives of their unknowns are called differential equations. In this curricular unit, a brief introduction to the quantitative theory of ordinary differential equations is made through the learning of tools and methods of solving them. Some of the examples and models presented have a framework in the areas of Engineering, Chemistry, Physics, Biology and Economics.

Not applicable

1. Introduction - Definition and classification of differential equations - Solution of a differential equation - Initial value problem (IVP) - Existence and uniqueness of solution of an IVP   2. First-order differential equations - Linear equations - Separable equations - Exact equations - Reducible to exact equations - Autonomous equations with one parameter and bifurcation diagrams   3. Second-order linear differential equations - Homogeneous equations with constant coefficients: characteristic equation and method of reduction of order - Nonhomogeneous equations: method of undetermined coefficients and method of variation of parameters - Mathematical modelling of some mechanical systems   4. Systems of first-order linear differential equations - Homogeneous systems: fundamental matrices - Nonhomogeneous systems: method of multidimensional variation of parameters - Phase portrait of homogeneous planar systems with constant coefficients

Creation and availability of short videos on topics related to the subject taught, as well as historical curiosities, playful problems and applications to the real world.

- BRAUN, M. (1993). Diffential Equations and Their Applications (4th ed.). Springer.