• 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 exampes from different disciplines such as mechanics, fluid dynamics, heat transfer, chemical kinematics 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.

The master has had a modification of the curriculum to improve and update the contents of the courses. This means that there are some credit changes in courses that share a classroom and / or nomenclature changes in some courses. In the cases that this happens, there are no substantial changes in the contents, although some additional activity may be requested for the 6-credit courses.

• 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: Dr. Jordi Villadelprat ( http://www.gsd.uab.es/index.php?option=com_jresearch&view=member&task=show&former=0&id=33&Itemid=2 );
• Dra. Dolors Puigjaner (http://deim.urv.es/~dpuigja/ )
• 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
• Models of single populations
• Phase-plane analysis
• Linearization analysis
• Basic heat models
• Time dependent heat problems
• Heat conduction problems
• Introduction to partial differential equations

• 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 the student's personal work and presupposes authenticity of authorship and originality of the exercises completed.

Lack of authenticity of authorship or originality of assessment tests, copying or plagiarism, the fraudulent attempt to obtain a better academic result, collusion to copy or concealing or abetting copying, use of unauthorized material or devices during assessment, inter alia, are offences that may lead to serious academic or other sanctions.

Firstly, you will fail the course (D/0) if you commit any of these offences when completing activities defined as assessable in the course plan, including the final tests. Offences considered to be misconduct include, among others, the use of unauthorized material or devices during the tests, such as social media or internet search engines, or the copying of text from external sources (internet, class notes, books, articles, other students' essays or tests, etc.) without including the corresponding reference.

And secondly, the UOC's academic regulations state that any misconduct during assessment, in addition to leading to the student failing the course, may also lead to disciplinary procedures and sanctions.

The UOC reserves the right to request that students identify themselves and/or provide evidence of the authorship of their work, throughout the assessment process, and by the means the UOC specifies (synchronous or asynchronous). For this purpose, the UOC may require students to use a microphone, webcam or other devices during the assessment process, and to make sure that they are working correctly.

The checking of students' knowledge to verify authorship of their work will under no circumstances constitute a second assessment.

• View the assessment model