Calculus I, Calculus II, Linear Algebra.

By the end of this course, students will be able to: 1. Know and understand the mathematical principles of the Theory of Differential Equations, both Ordinary and in Partial Derivatives, underlying Energy Engineering. 2. Apply their knowledge and understanding of the mathematical principles to identify, formulate and solve problems in Differential Equations by using established methods. 3. Combine theory and practice to solve Differential Equations problems. 4. Know and understand the methods and procedures of the Theory of Differential Equations, its area of application and its limitations.

1. First Order Differential Equations. a. Definitions and examples. b. Elementary resolution methods. c. Applications. 2. Higher Order Linear Differential Equations. a. Linear equations of order n with constant coefficients. b. Equations with variable coefficientes: undetermined coefficients and variation of constants 3. Laplace Transform. a. Definition and properties. b. Transforming and anti-transforming. c. Application to solving linear differential equations and systems. 4. Introduction to Partial Differential Equations. a. Initial and boundary problems. b. Examples of PDEs of Mathematical Physics. c. Different kind of equations and data. d. Classification of second order, linear PDEs. 5. Method of separation of variables. a. Even, odd, and periodic extensiones of a function. Trigonometric Fourier series. b. Solving homogeneous and non-homogeneous PDEs using separation of variables and Fourier series. 6. Sturm-Liouville Problems. a. Self-adjoint Sturm-Liouville problems. b. Rayleigh's quotient. Minimization theorem. c. Solving PDEs using separation of variables and generalized Fourier series.

The learning methodology consists of: -lectures covering the most important topics defined in the course programe. -Participation at class solving proposed problems in group or individually on the blackboard.