PHBA8240 Complex stimulus control - research and application Emneplan

A student who has completed this course should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

On successful completion of the course the student:

• knows the relevance of a selection of mathematical models to real-world phenomena
• has a thorough understanding of how mathematical modelling and scientific computing are utilized in various industrialized settings
• has a repertoire of methods to solve and/or analyze ordinary and partial differential equations (ODEs and PDEs)
• knows how to analyze the dynamics of an ODE system

Skills

On successful completion of this course the student:

• is able to derive mathematical models from facts and first principles for a selection of dynamical systems
• can apply mathematical modelling techniques on scenarios relevant to industry
• can implement mathematical models within the context of applied computer and information technology
• is able to analyse ODE systems and use bifurcation theory to elucidate the qualitative behavior of the systems
• can solve and/or analyse selected PDE models
• is able to implement and use a selection of numerical methods for solving ODEs and PDEs

General competence

On successful completion of this course the student:

• is aware of the usefulness and limitations of mathematical modelling as well as of pitfalls frequently encountered in modelling and simulation
• is able to discuss properties of a system using the equations of the mathematical model
• can explain and use numerical methods and interpret results of numerical simulations

The course is organized as a series of lectures and seminars where the subject material is presented and discussed. Between these sessions the students should work with problem solving, implementation of numerical methods and model simulations. The last part of the semester, students will work with a compulsory individual project supervised by the course lecturer. The project will involve studies and analyses of a mathematical model and a rather extensive implementation of the numerical solution of the model and result in a report.

The course consists of 1 introductory meeting, and 6 - 12 seminars of 4 x 45 minutes, and time for discussion and a final seminar (4 x 45 minutes). The introductory meeting takes place 2 weeks ahead of the main part of the course. At this meeting, the structure, content and purpose of the course are presented. The students are asked to give short presentations of their Ph.D. projects, and describe how the course is relevant to it. The main purpose of this early session is to help the students to start systematic work with the course readings.

The seminars target central themes from the course readings for discussion and reflection. A high level of student participation is expected. During this time, students will produce several reaction papers (3 - 4 pages double spaced), and a final presentation of one central theme from the course. Themes are assigned by the lecturers.

The final seminar consists of a discussion of the presentations, which are distributed in advance as papers not to exceed 10 pages double spaced, and introduced by each candidate in a short (3 minute) session. Course teachers mediate the discussions.

• All papers approved,
• attendance in at least 80 % of the seminars, and
• approved paper presentation in final seminar.

Portfolio.

Portfolio requirements: 4 reaction papers

All

Two internal examiners will assess the individual report and the oral presentation. External examiner is used periodically.

• Approaches to scientific computing and implementation of mathematical models
• Principles of modelling and derivation of mathematical models
• Analysis, numerical solution and bifurcations of ODEs
• Analysis and solution of linear PDEs
• Numerical methods for computation of solutions of ODEs and PDEs