TecnoCampus Foundation
eCampus
University Business
eCampus

What are you looking for?

General information

Subject type: Basic

Coordinator: Joan Triadó Aymerich

Trimester: First term

Credits: 6

Teaching staff: 

Moses Burset Albareda
Bernat Vilert Bosch 

Academic year: 2025

Teaching course: 1

Languages ​​of instruction

  • Catalan

Competencies / Learning Outcomes

Specific skills

  • K2. Identify the basic methodologies of linear algebra; geometry; differential geometry; differential and integral calculus; differential and partial differential equations; numerical methods; numerical algorithm; statistics, and optimization that are applied in engineering.

  • S1. Solve, through the use of mathematics and statistics, the possible problems that may arise in engineering.

  • S31. Apply critical thinking using different strategies depending on what needs to be learned and in the context in which it needs to be learned.

Presentation of the subject

It is an introductory course in linear algebra and differential calculus with the purpose of leveling students' mathematical knowledge and laying a firm methodological basis for developing the calculations needed in engineering.

Tecnocampus will provide teachers and students with the digital tools needed to carry out the course, as well as guides and recommendations that facilitate adaptation to the non-contact mode, if necessary.


 

Contents

Topic 1: Vector spaces
  Coordinate systems
  Euclidean vector space
  Generalization of the vector concept
  Linear dependence of vectors. Bases
  Values ​​and vectors of a square matrix

Topic 2: Systems of linear equations
  Operations with matrices
  Gauss and Gauss-Jordan method
  Definition and properties of determinants
  Cramer's rule

Topic 3: Real functions
  Definition and graphics
  Function transformation
  Examples of functions
  Limit of a function
  Continuity of a function

Topic 4: Derivation of real functions
  Definition of derivative
  Basic rules of derivation
  Concepts associated with the second derivative
  Indeterminate forms of limits (Rule of the Hospital)

Topic 5: Sequences and series
  Concept of succession
  Limit of a succession
  Series
  Power series
  Polynomial approximation of functions
 

Activities and evaluation system

-First (partial) individual exam: 35%
- Second (final) individual exam: 35%
-Individual questions: 30%

If in the partial exam (algebra) the grade was equal to or higher than 5, you can choose to take the whole final exam or just the second part (analysis). If the first part grade was lower than 5, the final exam will be 70% of the grade and the entire subject will be evaluated.

During the course, individual questions will be assessed (minimum 2 per student) that will represent 30% of the final grade (oral exam type)

If in the final exam the grade is not higher than 5, you will have to go to the recovery exam, regardless of the other grades of the course.

The maximum grade that can be obtained in the recovery exam will be 8.

The individual questions will not be able to be recovered. 

 

Important: 

Any form of academic fraud will be sanctioned in accordance with the center's assessment regulations. If signs of fraud are detected, including the improper use of generative artificial intelligence tools, the subject's teaching staff may call the student for an individual interview with the aim of verifying their authorship.

Bibliography

Basic

Course notes (available on the virtual campus)

Steiner, Erich. Mathematics for applied sciences. Ed. Reverté (Barcelona, ​​2003) ISBN: 84-291-5159-1

Complementary

Lay, David C; Murrieta Murrieta, Jesús Elmer. Linear algebra and its applications. Ed. Pearson (3rd ed), 2007. (https://dokumen.tips/download/link/algebra-lineal-y-sus-aplicaciones-3ra-edicion-david-c-lay-56327c66f18ec.html)

M. Krasnov et al. Higher mathematics course for engineers. Ed. look (1990)