Universitat Politècnica de Catalunya · BarcelonaTech

Mathematics I (2500208) – Course 2025/26 PDF

Syllabus

Learning Objectives

Mathematical resources are provided to understand natural environmental processes, with special emphasis on the functions of several variables, as well as some basic programming notions. Numerical methods for functional approximation and numerical integration will also be discussed.

Competencies

Especific

Solve mathematical problems that may arise in engineering by applying knowledge about: linear algebra, geometry, differential geometry, differential and integral calculus, optimization, ordinary differential equations.

Obtain basic knowledge about the use and programming of computers, operating systems, databases and basic numerical calculation and applied to engineering.

Manage the basic concepts about the general laws of mechanics and thermodynamics, concept of field and heat transfer, and apply them to solve engineering problems.

Apply the basic principles of general chemistry, organic and inorganic chemistry and their applications in engineering.

Describe the global functioning of the planet: atmosphere, hydrosphere, lithosphere, biosphere, anthroposphere, biogeochemical cycles (C, N, P, S), soil morphology and apply it to problems related to geology, geotechnics, edaphology and climatology.

Generic

Identify, formulate and solve problems related to environmental engineering.

Apply the functions of consulting, analysis, design, calculation, project, construction, maintenance, conservation and exploitation of any action in the territory in the field of environmental engineering.

Apply business management techniques and labor legislation.

Total hours of student work

Hours Percentage
Supervised Learning Large group 30h 50.00 %
Medium group 30h 50.00 %
Self Study 90h

Teaching Methodology

The course consists of 2 hours per week of classroom activity (large size group) and 2 hour weekly with half the students (medium size group). The 2 hours in the large size groups are devoted to theoretical lectures, in which the teacher presents the basic concepts and topics of the subject, shows examples and solves exercises. The 1 hour in the medium size groups is devoted to solving practical problems with greater interaction with the students. The objective of these practical exercises is to consolidate the general and specific learning objectives. The rest of weekly hours devoted to laboratory practice. Support material in the form of a detailed teaching plan is provided using the virtual campus ATENEA: content, program of learning and assessment activities conducted and literature. 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 grade for the course will consist of: - Practical works and classwork (NA). - Two exams (NE1 and NE2). 1. The practical work (NA) will include, among others, the resolution of problems and the performance of directed work. 2. The contents of the NE1 and NE2 exams will be in accordance with all the subject taught from the beginning of the course. - The NE1 exam will be taken approximately halfway through the semester and the subject taught so far will enter. - The NE2 exam will be a final exam, where the complete subject taught throughout the course will enter. The note of the exams will be calculated as: NE =0.5 * NE1 + 0.5 * NE2 The final grade for the course will be: Final Note = 0.3 * NA + 0.7 * NE Criteria for re-evaluation qualification and eligibility: students that failed the ordinary evaluation and have regularly attended all evaluation tests will have the opportunity of carrying out a re-evaluation test during the period specified in the academic calendar. Students who have already passed the test or were qualified as non-attending will not be admitted to the re-evaluation test. The maximum mark for the re-evaluation exam will be five over ten (5.0). The non-attendance of a student to the re-evaluation test, in the date specified will not grant access to further re-evaluation tests. Students unable to attend any of the continuous assessment tests due to certifiable force majeure will be ensured extraordinary evaluation periods. These tests must be authorized by the corresponding Head of Studies, at the request of the professor responsible for the course, and will be carried out within the corresponding academic period.

Test Rules

Students who fail the regular assessment who have regularly taken the assessment tests of the failed subject will have the option of taking a re-assessment test in the period set in the academic calendar. Students who have already passed it or students who have qualified as not presented will not be able to take the re-assessment test for a subject. The maximum grade in the case of reassessment will be five (5.0). The non-attendance of a student summoned to the re-evaluation test, held in the fixed period, will not be able to give rise to the realization of another test with later date. Extraordinary assessments will be conducted for those students who due to accredited force majeure have not been able to complete some of the continuous assessment tests. These tests must be authorized by the corresponding head of studies, at the request of the teacher responsible for the subject, and will be carried out within the corresponding teaching period. Once each exam has been taken, there is the possibility that a student may be called to do an oral interview as a validation of their written exam, this interview being on the subject of the exam. In case of not obtaining a satisfactory assessment in the interview, the exam will be given as failed with a grade of zero.

Office Hours

It will be made public at the beginning of the course

Bibliography

Basic