## 26405 - Mathematics

### Teaching Plan Information

2017/18
Subject:
26405 - Mathematics
Faculty / School:
Degree:
296 - Degree in Geology
ECTS:
8.0
Year:
1
Semester:
Annual
Subject Type:
Basic Education
Module:
---

### 5.1. Methodological overview

1      Theoretical classes with the development of case studies.

2      Problem solving classes.

3      Computer practices in which the student uses free scientific calculation programs (OCTAVE , SAGE or similar )

4      Subject program with the following blocks:

• FUNCTIONS
• LIMITS AND CONTINUITY
• DIFFERENTIAL CALCULUS OF ONE VARIABLE FUNCTIONS
• INTEGRAL CALCULUS OF ONE VARIABLE FUNCTIONS
• LINEAR ALGEBRA

Formative activity 1: Acquisition of basic knowledge of mathematics.

Methodology: Participatory Lectures in large group; Tutorials (small and/or individual groups).

Formative Activity 2: Problem Solving and analysis of case studies.

Methodology: problem-based learning. Teamwork and individual.

Formative Activity 3: Use of scientific calculation programs for problem solving. Methodology: Learning to manage scientific calculation programs. Work experience

### 5.3. Syllabus

- Elementary functions. Graphs.

- Limits of functions. Continuity. Bisection method.

- Derivatives. Calculation and geometric and physical interpretation. Application of derivatives: maximum and minimum. Newton method. Interpolation.

- Indefinite integrals. Change of variable, integration by parts, integrals of rational and trigonometric functions.

- Definite integral. Barrow’s rule. Applications: Areas, volumes and lengths. Numerical integration.

- Matrices. Operations. Properties.

- Determinants. Cramer's rule.

- Linear systems. Gauss’ method. Least squares method.

- Eigenvalues and eigenvectors.

### 5.4. Course planning and calendar

Schedule sessions and presentation of works:

• Theoretical classes and problems: twice a week
• Computer sessions: classes of 1-2 hours in small groups
• Meetings with the teacher to deal about the subject

( NOTE : the specific dates will be updated when available)

### 5.5. Bibliography and recommended resources

 BB Kolman, Bernard. Álgebra lineal / Bernard Kolman, David R. Hill ; traducción, Víctor Hugo Ibarra Mercado ; revisión tecnica, Alfonso Bustamante Arias... [et al.] . - [8ª ed.] México [ etc.] : Pearson, 2006 BB Larson, Ron. Cálculo y geometría analítica / Roland E. Larson, Robert P. Hostetler, Bruce H. Edwards ; con la colaboración de David E. Heyd ; traducción, Lorenzo Abellanas Rapún . - 6ª ed. en español Madrid [etc.] : McGraw-Hill, D.L. 1999 BB Nakos, George. Algebra lineal con aplicaciones / George Nakos, David Joyner . México : International Thomson Editores, cop. 1999 BB Neuhauser, Claudia. Matemáticas para ciencias / Claudia Neuhauser ; traducción, Ana Torres Suárez . 2ª ed., reimp. Madrid [etc.] : Pearson Prentice Hall, D.L. 2009 BB Nicholson, W. Keith. Algebra lineal con aplicaciones / W. Keih Nicholson ; traducción Julián Martínez Valero ; revisión técnica Juan Llovet Verdugo . 4ª ed. BB Strang, Gilbert. Algebra lineal y sus aplicaciones / Gilbert Strang ; versión española de Manuel López Mateos, con la colaboración de Margarita de Meza . Madrid [etc.] : Addison-Wesley Iberoamericana, D.L. 1989 BB Zill, Dennis G.. Cálculo con geometría analítica / Dennis G. Zill ; traductor Eduardo Ojeda Peña ; revisores técnicos Bertha Dávila de Apodaca ... [et al.] México, D.F. : Iberoamérica, cop. 1987

 LISTADO DE URLs: http://descartes.cnice.mec.es/ - [http://descartes.cnice.mec.es/] http://integrals.wolfram.com/ - [http://integrals.wolfram.com/] http://mathworld.wolfram.com/ - [http://mathworld.wolfram.com/] http://thales.cica.es/rd/ - [http://thales.cica.es/rd/] http://www.aulafacil.com/ - [http://www.aulafacil.com/] http://www.dma.fi.upm.es/mreyes/Algebra/ - [http://www.dma.fi.upm.es/mreyes/Algebra/] http://www.inetor.com/ - [http://www.inetor.com/] http://www.oei.es/ - [http://www.oei.es/] http://www.vitutor.com/ - [http://www.vitutor.com/]