• Description

This course aims to provide the student with some skills required to develop mathematical models of problems that have their origin in various areas such as engineering, physics or economics. The emphasis of the course is on those mathematical techniques that involve differential equations to understand physical problems. We have aimed to include practical examples from different disciplines such as  heat transfer or population growth. The course focuses on three issues: the mathematical formulation of the empirical model, the mathematical resolution of the resulting differential equation by analytical or numerical and the analysis and interpretation of the results.

• Prior knowledge

Some basic calculus and algebra are required. Students must also be able to read and understand scientific texts written in English.

• Information prior to enrolment

• Coordinating teachers: Dra. Dolors Puigjaner (https://orcid.org/0000-0001-5251-2022 )
• Credits: 6

• Learning objectives and results

The main goal of the course is to provide the student with some basic modelling skills, which have application to a wide variety of problems. The course focuses on models that involve formulating, solving and analyising differential equations which describe rates of change. However, the skills developed are transferable to many other areas.

• Content

• Compartmental models
• Time dependent heat problems
• Heat conduction and diffusion problems
• Models of single populations
• Phase-plane analysis

• Additional information on support tools and learning resources

• Matlab software
• Videos from http://www.chaos-math.org/en

• Guidelines on assessment at the UOC

Assessment at the UOC is, in general, online, structured around the continuous assessment activities, the final assessment tests and exams, and the programme's final project.

Assessment activities and tests can be written texts and/or video recordings, use random questions, and synchronous or asynchronous oral tests, etc., as decided by each teaching team. The final project marks the end of the learning process and consists of an original and tutored piece of work to demonstrate that students have acquired the competencies worked on during the programme.

To verify students' identity and authorship in the assessment tests, the UOC reserves the right to use identity recognition and plagiarism detection systems. For these purposes, the UOC may make video recordings or use supervision methods or techniques while students carry out any of their academic activities.

The UOC may also require students to use electronic devices (microphones, webcams or other tools) or specific software during assessments. It is the student's responsibility to ensure that these devices work properly.

The assessment process is based on students' individual efforts, and the assumption that the student is the author of the work submitted for academic activities and that this work is original. The UOC's website on academic integrity and plagiarism has more information on this.

Submitting work that is not one's own or not original for assessment tests; copying or plagiarism; impersonation; accepting or obtaining any assignments, whether for compensation or otherwise; collaboration, cover-up or encouragement to copy; and using materials, software or devices not authorized in the course plan or instructions for the activity, including artificial intelligence and machine translation, among others, are examples of misconduct in assessments that may have serious academic and disciplinary consequences.

If students are found to be engaging in any such misconduct, they may receive a Fail (D/0) for the graded activities in the course plan (including final tests) or for the final grade for the course. This could be because they have used unauthorized materials, software or devices (such as artificial intelligence when it is not permitted, social media or internet search engines) during the tests; copied fragments of text from an external source (the internet, notes, books, articles, other students' work or tests, etc.) without the corresponding citation; purchased or sold assignments, or undertaken any other form of misconduct.

Likewise and in accordance with the UOC's academic regulations, misconduct during assessment may also be grounds for disciplinary proceedings and, where appropriate, the corresponding disciplinary measures, as established in the regulations governing the UOC community (Normativa de convivència).

In its assessment process, the UOC reserves the right to:

• Ask students to provide proof of their identity as established in the UOC's academic regulations.
• Ask students to prove the authorship of their work throughout the assessment process, in both continuous and final assessments, through a synchronous oral interview, of which a video recording or any other type of recording established by the UOC may be made. These methods seek to ensure verification of the student's identity, and their knowledge and competencies. If it is not possible to ensure the student's authorship, they may receive a D grade in the case of continuous assessment or a Fail grade in the case of the final assessment.

Artificial intelligence in assessments

The UOC understands the value and potential of artificial intelligence (AI) in education, but it also understands the risks involved if it is not used ethically, critically and responsibly. So, in each assessment activity, students will be told which AI tools and resources can be used and under what conditions. In turn, students must agree to follow the guidelines set by the UOC when it comes to completing the assessment activities and citing the tools used. Specifically, they must identify any texts or images generated by AI systems and they must not present them as their own work.

In terms of using AI, or not, to complete an activity, the instructions for assessment activities indicate the restrictions on the use of these tools. Bear in mind that using them inappropriately, such as using them in activities where they are not allowed or not citing them in activities where they are, may be considered misconduct. If in doubt, we recommend getting in touch with the course instructor and asking them before you submit your work.

• View the assessment model