• 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

The assessment process is based on students' own work and the assumption that this work is original and has been carried out by them.

In assessment activities, the following irregular behaviours, among others, may have serious academic and disciplinary consequences: someone else being involved in carrying out the student's assessment test or activity, or the work being not entirely original; copying another's work or committing plagiarism; attempting to cheat to obtain better academic results; collaborating in, covering up or encouraging copying; or using unauthorized material, software or devices during assessment.

If students are caught engaging in any of these irregular behaviours, they may receive a fail mark (D/0) for the assessable activities set out in the course plan (including the final tests) or in the final mark for the course. This could be because they have used unauthorized materials, software or devices (e.g. social networking sites or internet search engines) during the tests, because they have copied text fragments from an external source (internet, notes, books, articles, other student's projects or activities, etc.) without correctly citing the source, or because they have engaged in any other irregular conduct.

In accordance with the UOC's academic regulations , irregular conduct during assessment, besides leading to a failing mark for the course, may be grounds for disciplinary proceedings and, where appropriate, the corresponding punishment, as established in the UOC's coexistence regulations.

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

• Ask the student to provide proof of their identity, as established in the university's academic regulations.
• Request that students provide evidence of the authorship of their work, throughout the assessment process, both in continuous and final assessment, by means of an oral test or by whatever other synchronous or asynchronous means the UOC specifies. These means will check students' knowledge and competencies to verify authorship of their work, and under no circumstances will they constitute a second assessment. If it is not possible to guarantee the student's authorship, they will receive a D grade in the case of continuous assessment or a Fail in the case of final assessment.

  For this purpose, the UOC may require that students use a microphone, webcam or other devices during the assessment process, in which case it will be the student's responsibility to check that such devices are working correctly.

• View the assessment model