TecnoCampus Foundation
eCampus
University Business
eCampus

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General information

Subject type: Basic

Coordinator: Vladimir Bellavista Parent

Trimester: Third term

Credits: 6

Teaching staff: 

Jaume Dolcet I Monés

Academic year: 2025

Teaching course: 1

Languages ​​of instruction

  • Spanish
  • Catalan

Teaching will be given in Catalan or Spanish depending on the teaching staff. 

Competencies / Learning Outcomes

Basic skills

  • B1_That students have demonstrated knowledge and understanding in a field of study that is based on general secondary education, and is accustomed to finding at a level that, although with the support of advanced textbooks, also include some aspects that involve knowledge from the forefront of your field of study

  • B3_Students have the ability to gather and interpret relevant data (usually within their area of ​​study), to make judgments that include reflection on relevant social, scientific or ethical issues

  • B4_That students can convey information, ideas, problems and solutions to both specialized and non-specialized audiences

Specific skills

  • EFB1_Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge about: linear algebra, differential and integral calculus, numerical methods, numerical algorithms, statistics and optimization

Transversal competences

  • T1_That students know a third language, which will be preferably English, with an adequate level of oral and written form, according to the needs of the graduates in each degree

Presentation of the subject

The course reviews and expands the knowledge that students already have in high school about functions, derivation and integration of functions, series and numerical methods.

Contents

Topic 1. Real functions of a real variable

  1. Generalities
  2. Limit and continuity of a function
  3. Bisection method for root calculation

Topic 2. Derivation of real functions of a real variable

  1. The derivative
  2. Basic rules of derivation
  3. Newton's method for calculating roots
  4. Function ends
  5. Growth and degrowth of functions
  6. Concavity and convexity of functions. Turning points
  7. Representation of functions
  8. Indeterminate forms of limits. Hospital Rule

Topic 3. Successions and series

  1. successions
  2. Series
  3. Series of powers. Polynomial approximation of functions

Topic 4. Integration of functions

  1. Indefinite integral.
  2. Integral defined
  3. Numerical integration

Activities and evaluation system

75% Exams: At least a 4 must be obtained in each partial, and the arithmetic average of the partials must be at least 5. Partial exam 1 corresponds to 40% and partial exam 2 to 35%.

25% Exercises done in class individually or in groups. Non-returnable activity. They must all be submitted to average and pass.

Final grade: NF = 0.40 E1 + 0.35 E2 + 0.25 E3, the course will be passed with NF >= 5

Recovery: 
NR = 0.40 E1 + 0.35 E2 + 0.25 E3 or NR = 0.75 (E1+E2) + 0.25 E3
the course will be passed with NR=5

Considerations:

1.- In general, Tecnocampus establishes: any form of academic fraud will be sanctioned in accordance with the center's evaluation regulations. In the event that 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.

2.- In the particular case of this subject, given its fundamental nature, the student is required not only to provide solutions to certain problems, but also to be able to generate them autonomously, without any external help. For this reason, the use of generative artificial intelligences (IAG) to resolve the problems posed in the subject —whether in exercises, practices or tests— is counterproductive, is strictly prohibited and will be considered a case of fraud due to plagiarism. The critical use of IAGs as a vehicle to resolve doubts about the subject is not considered a misuse of these mechanisms as long as this does not contradict what has been indicated above and the student does not lose sight of the fact that he may obtain incorrect and/or non-adjusted answers to the contents of the subject. Failure to comply will result in a NP grade for the subject -without the right to retake-.

3.- It will also lead to a NP grade in the subject if the student uses unauthorized tools, such as electronic devices, during the exams.

Bibliography

Basic

Larson, R; Edwards, BH (2010) Calculus I of a variable. 9th ed. McGraw-Hill

 

Smith, Robert T; Minton, Roland B. (2003) Calculus. 2nd ed. McGraw Hill

Spivak, M. (2006). calculus Cambridge University Press.

Tan, Soo T. (2011) Calculus: Early Transcendentals. Brooks / Cole.