Degree in Telematics (Networks and Internet Technologies)

Degree in Telematics (Networks and Internet Technologies)

Become an expert engineer in Network and Internet Technologies and get the CCNA and CCNP official qualifications

Statistics and Mathematical Analysis

Every graduate should master fundamental mathematical tools in engineering-related knowledge areas as diverse as signal and image processing, acoustics, digital communications, computer graphics or artificial intelligence. The objective of the course is to give an advanced vision of the mathematical tools that a technology degree requires. The course comprises three large blocks: functions of several variables, multiple integrals, and probability and statistics. The blocks of functions of several variables and of multiple integration constitute the part of the subject dedicated to mathematical analysis, and are taught during the first semester of the course. The probability and statistics block is taught during the second semester of the course.
Type Subject
Tercer - Obligatoria

Titular Professors

Previous Knowledge

Differential and Integral one variable functions calculus. Vectors spaces and their basic properties.


Learning Outcomes of this subject are:

LO.1 Mathematical knowledge to face the degree.

This is a very generic learning outcome, which is also shared with other subjects. In this subject, this result of general learning is seggregated in these other two:

LO1.1: Knowledge of multivariate mathematical analysis, probability and statistics to face the degree.
LO1.2: Practical application of the acquired knowledge to problem solving.


Block 1. Functions of several variables
1. Previous definitions
2. Functions of several real variables
2.1. Definition and domain
2.2. Limits
2.3. Continuity
2.4. Graphs, level curves and surfaces
3. Total and partial increment of a function. Differential of a function
4. Partial derivatives
4.1. Definition
4.2. Geometric interpretation
4.3. Generalization to functions of more than two variables
4.4. Higher order partial derivatives
5. Differentiability
5.1. Errors and differentials
6. Directional derivative
6.1. Geometric definition and interpretation
6.2. Differentiability and directional derivative
6.3. Gradient: definition and properties
7. Tangent plane and line normal to a function
8. Derivation of implicit and composite functions
9. Maxima and minima
10. Constrained optimization. Lagrange multipliers method

Block 2. Multiple integrals
1. Double integrals
1.1. Domain and properties
1.2. Calculation of double integrals
1.3. Change of variable. Jacobians. Polar coordinates
2. Triple integrals
2.1. Domain and properties
2.2. Calculation of triple integrals
2.3. Change of variable. Cylindrical and spherical coordinates

Block 3. Probability and statistics
1. Combinatorics
1.1. Variations
1.2. Permutations
1.3. Combinations
2. Introduction to probability
2.1. Previous definitions
2.2. Operations between events
2.3. Definitions of probability
2.4. Conditional probability
2.5. Law of total probabilities
2.6. Bayes' theorem
2.7. Independent events
3. Random variable
3.1. Previous definitions
3.2. Discrete random variable
3.2.1. Distribution function
3.3. Continuous random variable
3.3.1. Distribution function
3.3.2. Density function
3.4. Mathematical expectation and moments
3.4.1. Expectation
3.4.2. Variance and standard deviation
3.5. Markov and Chebysev inequalities
4. Univariate distributions
4.1. Discrete distributions
4.1.1. Binomial
4.1.2. Poisson
4.2. Continuous distributions
4.2.1. Uniform
4.2.2. Normal
5. Bivariate distributions
5.1. Discrete distributions
5.2. Continuous distributions
5.3. Distribution functions (accumulated)
5.4. Marginal distributions
5.5. Independent random variables
5.6. Conditional distributions
5.7. Covariance and correlation
5.8. Linear regression between two random variables
6. Sample theory
6.1. Central limit theorem
6.2. Sampling
6.3. Hypothesis testing


The course is taught in 2 weekly lessons lasting 100 minutes each.

The usual dynamics of each class will consist of a combination of theoretical explanations always followed by exercises that exemplify what has just been explained. Applied methodologies: master class (MD0), problems and exercises class (MD1).

Additionally, the eStudy provides resources for the student to carry out self-learning activities (by viewing videos indexed according to their content) and self-assessment (by conducting non-evaluable questionnaires on the content). Applied methodology: self-paced learning (MD5).

Finally, in order to achieve an applied view of the mathematical concepts presented in class, two practical exercises using the Matlab software will be undertaken, one each semester. Applied methodology: challenge-based learning (MD11).


See the electronic folder of the subject.

Evaluation Criteria

See the electronic folder of the subject.

Basic Bibliography

All of the books listed below are available at the La Salle Library.

Blocks 1 and 2: Functions of multiple variables, Multiple integrals

• N. Piskunov, “Cálculo diferencial e integral,” Ed. Montaner & Simon
• G.L. Bradley, K.J. Smith, “Cálculo de varias variables,” Ed. Prentice Hall
• G.B. Thomas, R.L. Finney, “Cálculo – varias variables,” Ed. Addison Wesley Longman
• J. De Burgos, “Cálculo infinitesimal de varias variables”, Ed. Mc Graw Hill

Block 3: Probability and statistics
• L. Vicent, R. Villalbí, “Probabilitat”, available in PDF in the eStudy
• D.D. Wackerly, W. Mendenhall, R.L. Schaeffer, " Estadística matemática con aplicaciones." Ed. Math

Additional Material

1. Lliçons de Càlcul de Probabilitats. Marta Sanz. 1995.Publicacions Universitat de Barcelona.
2. Problemas de Probabilidades y Estadística. C.M. Cuadras. Ediciones PPU. 1990. Barcelona.
3. Problemas de Análisis Matemático. Bombal. Marín. Vera. Editorial AC, libros científicos y técnicos. Madrid.