Mathematics I is a mandatory subject within the basic module of the degree program. Its objective is to train students in the use of basic mathematical tools from Algebra and Calculus.



The horizontal and vertical coordination of the subject within the Module and the Degree will be ensured by the Degree Program Coordination Committee.

The aim is for students to develop the following competencies of the degree program:



1. Basic competencies defined in RD1393/2007 for the development of official university education.

2. Specific competencies of the Basic Module:

M01CM04 Understanding and use of basic mathematical tools and data analysis processes in a scientific environment.

PART I: Numerical Sets and Linear Algebra



Numbers: from natural numbers to complex numbers.

Algebraic structures: group, ring, field, vector space.

Homomorphisms.

Matrix diagonalization.



PART II: Real Functions of a Real Variable: Differentiation



Concept of function. Elementary functions.

Definition and rules of differentiation.

Applications of derivatives: Theorems. Taylor series. Growth, decay, and relative extrema.



PART III: Real Functions of a Real Variable: Integration



Antiderivative and indefinite integral.

Definite integrals. Fundamental Theorem of Calculus. Applications.

Improper integrals.

Both in lectures and classroom practice sessions, student participation is encouraged through appropriate questions and answers, problem-solving in class, etc.



On e-gela, online questions are posed to aid in the understanding of fundamental concepts and the use of mathematical language.

• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 100

Final written theoretical-practical exam (either in-person or by other means): 100%



WAIVER:

Failure to attend the final exam will result in forfeiture of the exam attempt.

Final written theoretical-practical exam (either in-person or by other means): 100%



WAIVER:

Failure to attend the final exam will result in forfeiture of the exam attempt.

Se indicará cada curso en la Guía Docente.

Basic bibliography

H. Anton, Introducción al Álgebra, Ed. Limusa



N. Piskunov, Cálculo diferencial e integral. Ed. Limusa, 2008.



M. Spivak, Calculus (Cálculo Infinitesimal), Ed. Reverté 2005



T. Apostol, Cálculo con funciones de una variable, con una introducción al álgebra lineal, Ed. Cátedra 1992

In-depth bibliography

M. Castellet e I. Llerena, Algebra Lineal y Geometría, Ed. Reverté 2000

J.M. Ortega, Introducción al Análisis Matemático, Ed. Labor Universitaria, 1993

B.P. Demidovich, 5000 Problemas de Análisis Matemático, Ed. Paraninfo 2003

Web addresses

www.geogebra.org
https://mathworld.wolfram.com/