Guia docente 2023_24 Escola de Enxeñaría de Telecomunicación

Contents

Topic	Sub-topic
Subject 1. Integral calculus in R.	The Riemann integral: integrable functions. Fundamental theorems of the integral calculus. Computation of primitives: integration by parts and change of variable. Improper integrals.
Subject 2. Numerical methods for the approximation of integrals.	Quadrature rules of interpolating polynomial type. Properties. Interpolation error. Particular cases: Poncelet, Trapezoidal and Simpson. Composite quadrature rules.
Subject 3. Fourier series and Fourier transform.	Orthogonal functions. Fourier series. Developments of Fourier series for odd and even functions. Convergence. The Fourier transform.
Subject 4. Multiple integration.	The double and triple integrals in elementary regions. Change in the order of integration. Theorems for the change of variable. Applications.
Subject 5. The Laplace transform.	Definition of the Laplace transform. Properties.
Subject 6. Ordinary differential equations.	Generalities on the differential equations: concept of solution, families of curves and orthogonal trajectories. Differential equations of first order: existence and uniqueness of solution, exact equations, separate variables, homogeneous equations and linear equations. Differential equations of second order: existence and uniqueness of solution for linear differential equations, application of the Laplace transform, indeterminate coefficients, variation of parameters, equation of Cauchy-Euler.