Programplaner og emneplaner - Student
PENG9570 Applied Mathematical Modelling and Analysis Course description
- Course name in Norwegian
- Applied Mathematical Modelling and Analysis
- Study programme
-
PhD Programme in Engineering Science
- Weight
- 10.0 ECTS
- Year of study
- 2022/2023
- Curriculum
-
SPRING 2023
- Schedule
- Programme description
- Course history
-
Introduction
Admission to the programme.
Recommended preliminary courses
A thorough knowledge of advanced calculus, including ordinary and partial differential equations. It is a great advantage if students are familiar with linear algebra and Fourier and Laplace transform theory. In terms of programming, some experience in implementing various numerical methods, including schemes for solving partial differential equations is recommended. Some knowledge of mathematical analysis, modern physics or physiology is recommended, depending on their specialisation.
Required preliminary courses
After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and competence:
Knowledge
The student is familiar with:
- the designer’s role in society and how design knowledge can contribute to different types of problem solving
- the different phases of a design project
- project planning as a basis for realising a design assignment
- problem formulation as a management tool
- different methods of increasing creativity
- basic methods of team work and good group dynamics
Skills
The student:
- is aware of his/her own and other people’s influence in group work
- knows basic terminology relating to design/the role of designers
- knows different methods of creative processes
- knows different techniques for making 2D and 3D sketches
Competence
The student:
- is familiar with relevant ethical issues such as privacy and copyright relating to the discipline and the profession and is aware of professional attitudes in the design field
- is capable of exchanging points of view and experience with others in the field and in this way contribute to developing good practice
- is capable of reflecting on his/her own development in the learning process and adjusting it
- is capable of working in a team on a joint topic towards a common goal
Learning outcomes
The work methods used in the different groups/design assignments will vary. In general, there will be:
- lectures
- team work with discussions on topics such as:
- needs, problems
- principle solutions (concepts) and ideas
- choice of solution
- presentation of solution
- work in 2D and 3D media
- physical modelling in suitable materials
- workshops
- papers and presentations
Content
Introductory module:
- Principles of modelling and derivation of mathematical models
- Analysis of ordinary differential equations (ODEs)
- Linear partial differential equations (PDEs)
- Prominent results from functional analysis and their application to ODEs and PDEs
- Numerical methods for computing of solutions of PDEs
Functional analysis:
- Completeness for normed spaces
- Hilbert spaces, compact and diagonalisable operators
- Theory of topological vector spaces
- Test functions, distributions and the Fourier transform
- Sobolev spaces and fundamental solutions of partial differential equations
Biosystems:
- Mathematical models for biological systems
- Analytical and numerical methods for simulation of system response
- Actuators and sensors for stimulation and measurements of biological systems
- Interaction of biological and measurement system
Modern physics:
- Monte Carlo techniques
- Splines and other expansion techniques
- Applications of expansions in spherical harmonics
- Numerical problems in general relativity and quantum physics
- Manifolds with geometric structures central to physics and engineering.
Within all specializations, the content may be adjusted to accommodate for the research area of each PhD candidate.
Teaching and learning methods
The following coursework is compulsory and must be approved in order to pass the exam:
- a minimum of 80% attendance in the Design Office project. The attendance requirement applies from when the students commence work in their respective teams. (last 4 weeks of the module (period 2)).
- oral presentation in groups where all group members contribute (period 1)
- reflection note
If the attendance requirement is not met, students must complete an additional written assignment. This assignment shall address:
- the design assignment
- the designer’s role
Course requirements
Practical exam in groups.
Through a group project in collaboration with fellow students in year two and three of the BA programme students are expected to develop proposals for solving real world assignments. Each group is tasked with an individual project from a unique client, all of which will have differing requirements. The group must identify which presentation formats and materials are most appropriate in order to communicate how solutions are to meet client needs. The module concludes with a visual group presentation, invariably supported by physical scale models and/or protypes; digital and/or other solutions. The work must be developed with consideration to client specifications; it must be relevant and contain all of the necessary elements ready for production and/or implementation.
Exam results cannot be appealed.
Assessment
All aids are permitted, as long as the rules for source referencing are complied with.
Permitted exam materials and equipment
Pass/fail.
Grading scale
One internal examiner. External examinator is used periodically.
Examiners
Two examiners. External examiner is used periodically.