TecnoCampus Foundation
eCampus
University Business
eCampus

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General information

Subject type: Basic

Coordinator: Julián Horrillo Tello

Trimester: First term

Credits: 6

Teaching staff: 

Moses Burset Albareda

Skills

Basic skills

  • B5_That students have developed those learning skills necessary to undertake further studies with a high degree of autonomy

     

Specific skills

  • E1_Training for the resolution of mathematical problems that may arise in engineering. Train to apply knowledge about: linear algebra; geometry; differential geometry; differential and integral calculus; differential equations and partial derivatives; numerical methods; numerical algorithm; statistics and optimization

Transversal competences

  • T2_That students have the ability to work as members of an interdisciplinary team either as one more member, or performing management tasks, in order to contribute to developing projects with pragmatism and a sense of responsibility, making commitments taking into account available resources

     

Description

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.


 

Learning outcomes

-Correctly apply fundamental concepts of differential and integral calculus, linear algebra and geometry, developing the ability to apply them to problems in engineering.

-Ability to use mathematical tools necessary in solving analytical and numerical problems.
 

Working methodology

Master classes combined with practical classes, where problems mainly applied to engineering will be solved. Face-to-face teaching.

 

Contents

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

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

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

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)

Successions and series
  Concept of succession
  Limit of a succession
  Series
  Power series
  Polynomial approximation of functions
 

Learning activities

Classes: theory development and interspersed practical examples (theoretical-practical classes). We will dedicate the last day of the week to solving exercises.

Examinations: due tests. A partial first (of a liberating character of subject) and an end (with only a part or with all the matter of the asignatura, if it has suspended the partial).

Evaluation exercises: sis exercises to deliver (will be done in class)
 

Evaluation system

70% - Exams (partial and final)

30% - Evaluation of individual exercises
 

REFERENCES

Basic

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

Lay, David C; Murrieta Murrieta, Jesús Elmer (2007). Linear algebra and its applications. 3ª ed. Pearson Education.

Smith, Robert; Minton, Roland. Calculation. 2nd ed. McGraw-Hill 2003. ISBN 978-84-481-3861-5

Notes of the subject