ACIT4310 Applied and Computational Mathematics Emneplan

The course will provide the students with an understanding of what a mathematical model is and how we use models to gain insights into systems and processes in science and engineering. The course will train the students in using analytical and computational methods for analyzing and solving differential equations and prepare them for developing, analyzing and simulating mathematical models in their own projects. The models and methods taught in this course are generic and applicable not only in science, but also in various industrial contexts.

No formal requirements over and above the admission requirements.

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.

None.

A compulsory project will be assessed along with an oral exam:

A part of this exam will consist in a brief presentation of the candidate's project. The project (report of 3000-5000 words and presentation) will count 50% of the final grade, while the remaining 50% will be based on the oral examination.

The oral exam cannot be appealed.

Both exams must be passed in order to pass the course.

At the oral exam, the candidate is allowed to make use of her/his own computer for the presentation.

For the final assessment a grading scale from A to E is used, where A denotes the highest and E the lowest pass grade, and F denotes a fail.

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