Guia docente 2018_19 Escuela de Ingeniería de Telecomunicación

Contents

Topic	Sub-topic
Topic 1. Introduction.	Sets of numbers and functions of one variable.
Topic 2. n-dimensional space.	Scalar product, norm. Vector product. Polar, cylindrical and spherical coordinates.
Topic 3. 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 4. Continuity of functions of several variables.	Functions of several variables. Limits. Continuity. Bolzano's theorem.
Topic 5. Derivatives of functions of one variable.	Derivatives of a function in a point. Derivative function, successive derivatives, properties. Chain rule. Implicit differentiation. Derivative of inverse functions.
Topic 6. Applications of the derivative.	Maxima and minima. Mean value theorem. L'Hopital's rule. Local study of the graph of a function. Taylor polynomials. Newton's method.
Topic 7. Differential of functions of several variables.	Directional derivatives. Partial derivatives. Jacobian matrix. The chain rule. Higher order derivatives. Differential operators.
Topic 8. Applications of the differential calculation.	Extreme values. Extreme values with equality constraints. Newton's method.