PENG9630 Internettarkitektur og målinger Emneplan

Students who complete the course are expected to have the following learning outcomes, defined in terms of knowledge, skills and general competence:

Knowledge

Upon successful completion of the course, the student:

• Possesses comprehensive knowledge in specific advanced mathematical methods within the realm of the course, supplementing their existing specialization in applying mathematical methods in applied sciences.
• Demonstrates an advanced command of mathematical methods relevant to their doctoral research, positioning them at the forefront of knowledge in their chosen field.

Skills

Upon successful completion of the course, the student can:

• Apply advanced theoretical knowledge and mathematical techniques to solve intricate problems encountered in the application of mathematical methods.
• Strategically plan and execute scholarly endeavors within the scope of their doctoral research project, employing advanced mathematical methodologies.
• Critically analyze existing mathematical theories, methods, and solutions, both in theory and practical application, fostering a deeper understanding of complex mathematical problems.

General competence

Upon successful completion of the course, the student:

• Demonstrates competence in conducting extensive literature reviews, engaging in self-directed study, and employing research-based learning methodologies in advanced mathematical concepts.
• Applies acquired knowledge and skills to tackle sophisticated tasks and projects encountered in the domain of advanced mathematical methodologies.
• Effectively communicates intricate mathematical concepts, analyses, and solutions to audiences with varying levels of mathematical expertise, showcasing the ability to bridge specialist and non-specialist communication gaps.
• Exhibits the capacity to recognize the necessity for innovation within the realm of advanced mathematical methodologies and can initiate innovative approaches within their expertise.

Bachelor's or master's degree in engineering science or related fields.

Students who complete the course are expected to have the following learning outcomes, defined in terms of knowledge, skills and general competence:

Knowledge

On successful completion of the course, the student:

• knows how mathematical models can be derived from facts and first principles.
• has a repertoire of methods to solve and/or analyse both ordinary differential equation (ODE) systems and certain partial differential equations (PDEs).
• is able to apply analytical and/or numerical solution methods for PDEs to models of heat transfer, wave propagation and diffusion-convection and discuss the relevance of these models to real-world phenomena.
• is able to construct and develop relevant models and discuss the validity of the models.

Skills

On successful completion of the course, the student can:

• can determine steady states of ODE systems and use linear approximation to elucidate the stability properties of these states.
• can solve and/or analyse selected PDE models.
• is able to implement and use some numerical methods for solving relevant PDEs.
• can devise the solution of certain composite quantitative problems.
• can disseminate results and findings in an accessible manner – both orally and in writing.

General competence

• 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 that describes the system.
• can explain and use numerical methods, know their strengths and weaknesses and interpret results of numerical simulations.

Individual oral examination.

The exam cannot be appealed.

The course consists of three modules.

In the first module, the course staff and guest lecturers will provide a high-level overview of different parts of the internet's architecture.

The second part is a set of practical exercises that are designed to match the topics discussed in the first module.

The third module will consist of a set of seminars, where students elaborate on different parts of the architecture and how they can be assessed and monitored.

An individual, oral examination. The examination will address both general topics from within the course and the specific project developed by the student.

The oral examination cannot be appealed.

Pass or fail.

Students should be aware that a master's degree in a related engineering discipline (electrical, construction, building services, architectural engineering or renewable energy) and relevant undergraduate courses covering the topics of basic indoor climate, and heat and mass transfer is recommended in order to complete this course.

Two examiners. External examiner is used periodically.

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.

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.