Educational guide 2023_24 Escola Tècnica Superior d'Arquitectura

Contents

Topic	Sub-topic
Numbers, successions and series.	Presentation of different sets of numbers. Successions Series Taylor series.
Parametric equations and polar coordinates.	Curves defined by parametric equations. Tangents and areas. Arc length. Polar coordinates. Areas and lengths in polar coordinates.
3D Functions	Cylindrical and spherical coordinates. Functions Curves in space. Derivatives and integrals of vector functions.
Derivation of functions in several variables.	Functions of several variables. Limits and continuity. Partial derivatives. Tangent planes and linear approximations. Chain rule. Directional derivatives. Gradient. Maximus and minimous. Lagrange multipliers.
Integration of functions in several variables.	Double integrals over regions. Integration in polar coordinates. Area of a surface. Triple integrals. Change of variables in multiple integrals.
Differential equations.	Definition and properties of differential equations. Linear differential equations of first and second order.
Vector spaces.	Definition of vector space. Vector subspaces. Bases and base changes. Grassman formula.
Linear applications	Definition of linear application. Core and image of a linear application. Matrix of a linear application.
Values and eigenvectors.	Definition of vector and eigenvalue. Characteristic polynomial. Diagonalization theorem. Applications.