Guia docente 2023_24 Escola de Enxeñaría de Telecomunicación

Contents

Topic	Sub-topic
Topic 1. Introduction.	Sets of numbers and functions of one variable.
Topic 2. Continuity of functions of one variable.	Limit of a function in a point. One-sided limits. Continuity. The intermediate value theorem. Bolzano's theorem. The bisection method.
Topic 3. Continuity of functions of several variables.	n-dimensional space. Inner product, Norm. Vector product. Functions of several variables. Limits. Continuity. Bolzano's theorem.
Topic 4. Derivatives of functions of one variable and applications of the derivative.	Derivatives of a function at a point. Derivative function, successive derivatives, properties. Chain rule. Implicit differentiation. Derivative of inverse functions. Maxima and minima. Mean value theorem. L'Hopital's rule. Local study of the graph of a function. Taylor polynomials. Newton's method.
Topic 5. Differential of functions of several variables.	Directional derivatives. Partial derivatives. Jacobian matrix. The chain rule. Higher order derivatives. Differential operators.
Topic 6. Applications of the differential calculus.	Extreme values. Extreme values with equality constraints. Newton's method.