Educational guide 2014_15 Escola de Enxeñaría de Telecomunicación

Contents

Topic	Sub-topic
Subject 1. Introduction.	Sets of numbers and functions of one variable. n-dimensional space. Polar, cylindrical and spherical coordinates.
Subject 2. Continuity of functions of one variable.	Limits. Continuity. Theorem of the intermediate value. Theorem of Bolzano. Method of bisection.
Subject 3. Continuity of functions of several variables.	Functions of several variables. Limits. Continuity. Theorem of Bolzano.
Subject 4. Derivation of functions of one variable.	Derivation of a function in a point. Derivative function, derivative successive, properties. Rule of the chain. Implicit derivation. Derivation of reverse functions.
Subject 5. Applications of the derivative.	Maxima and minimum. Theorem of the mean value. Rule of L'Hopital. Local study of the graphic of a function. Taylor polynomial. Method of Newton.
Subject 6. Differential of functions of several variables.	Directional derivatives. Partial derivatives. Jacobian matriz. Rule of the chain. Higher order derivatives. Differential operators.
Subject 7. Applications of the differential calculation.	Extreme values. Extreme values with equality constraints. Method of Newton.