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2022/2023

Mathematics

Code: 102808 ECTS Credits: 9
Degree Type Year Semester
2501915 Environmental Sciences FB 1 1

Contact

Name:
Pere Ara Bertran
Email:
pere.ara@uab.cat

Use of Languages

Principal working language:
catalan (cat)
Some groups entirely in English:
No
Some groups entirely in Catalan:
Yes
Some groups entirely in Spanish:
No

Teachers

Pere Ara Bertran
Joan Orobitg Huguet
Joaquin Martín Pedret

Prerequisites

High school math.

Objectives and Contextualisation

On one hand, we will review all fundamental concepts that have been worked at high school.. On the other hand, we will introduce some new concepts  (as differential equations o calcules in seeral variables). But the most important point will be the emphasis in the use of these techniques in the mathematical modelization of several areas of interest.

Competences

  • Adequately convey information verbally, written and graphic, including the use of new communication and information technologies.
  • Analyze and use information critically.
  • Collect, analyze and represent data and observations, both qualitative and quantitative, using secure adequate classroom, field and laboratory techniques
  • Demonstrate adequate knowledge and use the tools and concepts of mathematics, computer science and statistics to analyze and manage environmental issues.
  • Demonstrate concern for quality and praxis.
  • Demonstrate initiative and adapt to new situations and problems.
  • Learn and apply in practice the knowledge acquired and to solve problems.
  • Teaming developing personal values regarding social skills and teamwork.
  • Work autonomously

Learning Outcomes

  1. Adequately convey information verbally, written and graphic, including the use of new communication and information technologies.
  2. Analyze and use information critically.
  3. Demonstrate concern for quality and praxis.
  4. Demonstrate initiative and adapt to new situations and problems.
  5. Describe and use basic mathematical language.
  6. Learn and apply in practice the knowledge acquired and to solve problems.
  7. Observe, recognize, analyze, measure and adequately represent mathematical concepts.
  8. Properly use the rules of differentiation and integration of functions.
  9. Solve elementary differential equations.
  10. Solve geometric problems and space plan.
  11. Teaming developing personal values regarding social skills and teamwork.
  12. Use basic techniques of statistics and probability.
  13. Using the basic results of differential calculus in several real variables.
  14. Work autonomously

Content

1. Elementary functions

2. Exponential growth and other population models

3. Limits and continuity

4. The derivative and its applications

5. The integral and its applications

6. Introduction to differential equations

Methodology

The course will be semi-presential. The students will be able to have presential teaching during some specific days. The rest of the teaching will be on-line.

The student will receive exercises lists for the work in the problem sessions.

The teaching of the course will use in essential form the virtual campus as means of communication, as well as other virtual tools. The students that want to communicate with the professors by e-mail must use the institutional address provided by the university (@autonoma.cat).

Naturally, the students will be able to ask questions about the development of the course during the presential hours.

Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Activities

Title Hours ECTS Learning Outcomes
Type: Directed      
Problems and resolution of problems 25 1 2, 6, 4, 3, 1, 14, 11
Theory 50 2 5, 7, 9, 10, 8, 13, 12
Type: Autonomous      
Resolution of problems 60 2.4 2, 6, 4, 3, 1, 14, 11
Theory 44 1.76 5, 7, 9, 10, 8, 13, 12
To prepare partial exams and to realize partial exams 36 1.44 2, 6, 5, 7, 9, 10, 1, 8, 13, 12

Assessment

The following evaluation acts will be performed:

  1. Two partial exams with a weight of  30% each
  2. Several "quiz" test  with a total weight of 40%.

The students not getting 5 points in the continuous evaluation can go to a final exam of all the subject if  they have been previously evaluated of at least  2/3  of the total of the continuous evaluation. If the qualification of this exam is superior to the one obtained in the continuous evaluation, the final qualification will be the one coming from the recovery exam. If it's inferior, the final qualification will be the average between the continuous evaluation qualification and the recovery exam qualification. The students having 5 or more points in the continuous evaluation also can go to the final exam, but they need to be aware that the final qualification can then be inferior, and they can even fail the subject.

A student will be considered "presented" if has participated in activities leading to at least 2/3 of the qualification.

Assessment Activities

Title Weighting Hours ECTS Learning Outcomes
Exercises 40% 4 0.16 2, 6, 4, 3, 5, 7, 9, 10, 1, 14, 11, 8, 13, 12
Partial exam 1 30% 3 0.12 2, 6, 4, 3, 5, 7, 9, 10, 1, 14, 11, 8, 13, 12
Partial exam 2 30% 3 0.12 2, 6, 4, 3, 5, 7, 9, 10, 1, 14, 11, 8, 13, 12

Bibliography

Main text:  "Matemàtiques i modelització per a les Ciències Ambientals" by J. Aguadé. Free access from webpage of library UAB.

Secondary: Neuhauser, C., Matemáticas para ciencias. 2a, edición, Pearson, Prentice Hall.

Software

We will use the free software SAGE. Also we will use the ACME platform.