General information


Subject type: Basic

Coordinator: Alfonso Palacios González

Trimester: Third term

Credits: 6

Teaching staff: 

Joan Fabregas Peinado

Skills


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

Description


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.

Learning outcomes


The learning outcomes specify the specific measure of the competencies worked on.

This subject contributes to the following learning outcomes specified for the subject to which it belongs:

  • LO1: Become familiar with mathematical language and logic and know their applications in the field of computer science. Know how to accurately express mathematical concepts. Be able to understand a demonstration and perform demonstrations using various methods (particularly the last two points).
  • LO2: Know and understand the basic properties of real numbers and functions.
  • LO3: Know and be able to apply the main concepts and results of differential and integral calculus.
  • LO4: Know and understand the concepts related to the polynomial approximation of functions.
  • LO5: Know and be able to apply numerical techniques for the approximate solution of problems in functional calculus (1).
  • LO6: Plan oral communication, answer appropriately to the questions asked and write basic level texts with spelling and grammar correction. Properly structure the content of a technical report. Select relevant materials to prepare a topic and synthesize its content. Answer appropriately when asked questions.

Additionally, the subject also assesses the following learning outcome that is not present in the subject to which it belongs:

  • LO7: Plan and carry out group work with pragmatism and a sense of responsibility.

(1) The teachers of the subject will replace the functional calculation (from the mathematical point of view the calculation with functions, the variables of which are other functions) by the calculation with functions of real variable that is to which the rest of results refers of course learning. Suppose, therefore, that this is some kind of transcription error.

Working methodology


The classes will be master classes (development of the theory and practical examples) and participatory (conceptual questions, guided resolution of exercises and presentation of exercises by the students).

The activity “programming of numerical calculation methods” makes the students apply and value in group the numerical calculation knowledge exposed in class.

Contents


  1. Real functions of a real variable
    1. Generalities
    2. Limit and continuity of a function
    3. Bisection method for root calculation
  2. Derivation of real functions from 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
  3. Successions and series
    1. successions
    2. Series
    3. Series of powers. Polynomial approximation of functions
  4. Function integration
    1. Indefinite integral.
    2. Integral defined
    3. Numerical integration

Learning activities


  • Master class: development of theory and practical examples.
  • Participatory class: collaborative instruction with conceptual questions and resolution of exercises guided by the teacher (collect evidence of learning of almost all expected results, as a guide for self-assessment of the student and their active participation in class) .
  • Resolution and presentation of group exercises: resolution and presentation of exercises by students (collect evidence of all expected results, especially RA6 and RA7).
  • Programming of numerical calculation methods: group activity, preparation of programs that implement the different numerical calculation methods studied, assessment and comparison of results (collect evidence of learning outcomes RA5, RA6 and RA7).
  • Assessment tests: four tests, one per topic, which collect evidence of general learning (LO1), and more specific ones as indicated below:
    • Topic 1: RA2
    • Topic 2: RA3 (derivation)
    • Topic 3: LO4
    • Topic 4: RA3 (integration)

Evaluation system


65% of the activity Assessment tests, recoverable individually in the event of suspending the subject. You must obtain a minimum grade of 3,5/10 in this activity in order to pass the subject.

15% the activity of Resolution and presentation of group exercises. Not recoverable.

15% the activity of Programming numerical methods. Not recoverable.

5% active participation in class, assessed through conceptual questions. Recoverable through the Assessment Tests.

 

REFERENCES


Basic

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

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