# Fundamentals of Mathematics for Environmental Science (250554) – Course 2024/25 PDF

# Syllabus

## Learning Objectives

In this course, some basic mathematical aspects will be provided to understand the existing relationships between different environmental parameters. Emphasis will be placed on teaching a block of basic mathematical tools: matrices, differential calculus, integral calculus, and geometry. At the end of the course, the students should have: a) obtained knowledge and calculus skills on matrices and systems of linear equations, basic linear transformations in the plane and space, differential and integral calculus of real-valued real functions; b) acquired basic knowledge about the use of Matlab, having had to practice with problems posed in some of the subjects that make up the course program;

## Competencies

### Especific

To know and apply the lexicon and concepts of the Marine Sciences and Technologies and other related fields.

Establish a good practice in the integration of common numerical, laboratory and field techniques in the analysis of any problem related to the marine environment.

### Generic

Develop a professional activity in the field of Marine Sciences and Technologies.

Address in a comprehensive manner the analysis and preservation of the marine environment with sustainability criteria.

## Total hours of student work

Hours | Percentage | |||
---|---|---|---|---|

Supervised Learning | Large group | 30h | 50.00 % | |

Medium group | 30h | 50.00 % | ||

Self Study | 90h |

## Teaching Methodology

Theoretical classes will be given, solving problems and practices. The subject is face-to-face and the work in class will be evaluated, in addition to the exams proposed for the course. The participation in class will be very positive. Class attendance will not be enough to pass the subject, which means that the student must spend about 4 hours a week on a regular basis outside the classroom. Support material is used in the format of a detailed teaching plan through the ATENEA virtual campus: contents, programming of assessment activities and directed learning and bibliography. Each week will consist of 4h-regular sessions + 2h of workshop (where additional questions can be answered and clarified, some other problems can be solved, etc.). Although most of the sessions will be given in the language indicated, sessions supported by other occasional guest experts may be held in other languages.

## Grading Rules

The evaluation calendar and grading rules will be approved before the start of the course.

The mark of the subject will be obtained from: - Autonomous Work Activities (total mark: NTA, up to 10 points). - Two exams (E1 and E2, marks: NE1 and NE2, up to 10 points each). The contents of the exams E1 and E2 will be in agreement with all the material taught from the beginning of the course. The final grade of the subject will be: Final Grade= 0,4*NTA + 0,2*NE1 + 0,4*NE2 ADMISSION AND QUALIFICATION CRITERIA FOR REVALUATION: Students failed in regular evaluation that have been submitted regularly to the evaluation tests of the subject will have the option to carry out a reassessment test in the period set in the academic calendar Students who have already passed the subject cannot carry out re-evaluation exam. The maximum qualification in the case of re-evaluation will be five (5.0). The non-attendance of a student to the test of re-evaluation, celebrated in the fixed period, will not allow the accomplishment of another test with later date. Extraordinary assessments will be made for students who have not been able to complete some of the continuous assessment tests because of their proven accreditation. These tests must be authorized by the corresponding head of studies, at the request of the professor responsible for the subject, and will be carried out within the corresponding teaching period.

## Test Rules

Will be discussed at the beginning of the course.

## Bibliography

### Basic

- Rojo, J. Álgebra lineal. 2a ed. Madrid: McGrawHill, 2007. ISBN 978-84-481-5635-0.
- Hoffman, K.; Kunze, R. Álgebra lineal. México D.F.: Prentice-Hall, 1973. ISBN 9688800090.
- Jarauta, E. Análisis matemático de una variable: fundamentos y aplicaciones. Barcelona: Edicions UPC, 2000. ISBN 8483014106.
- Estela, M.R. Fonaments de càlcul per a l'enginyeria. Barcelona: Edicions UPC, 2008. ISBN 9788483019696.

### Complementary

- Burgos, J. Álgebra lineal y geometría cartesiana. 3a ed. Madrid: McGraw-Hill, 2006. ISBN 8448149009.
- Hernández, E.; Vázquez, M.J.; Zurro, M.A. Álgebra lineal y geometría. 3a ed. Madrid: Pearson, 2012. ISBN 978-84-7829-129-8.
- Stoll, M. Introduction to real analysis. Reading, Mass.: Addison-Wesley, 1997. ISBN 0673995895.
- Estela, M.R.; Saà, J. Cálculo con soporte interactivo en moodle. Madrid: Pearson Educación, 2008. ISBN 9788483224809.