ACIT4310 Applied and Computational Mathematics Course description

I dette emnet skal studenten dokumentere planlegging, gjennomføring og evaluering av et opplærings, helse- og omsorgstiltak gjennomført i praksis (VERPRA21).

Emnet går parallelt med VERPRA21. I løpet av praksisperioden arrangeres det seminardager med relevans for VERPRA21 og prosjekteksamen i VERB3200. Fokuset i seminarene er tilpasset hvor i praksisforløpet studenten er. Sentrale elementer i seminarene er kunnskapsbasert praksis og skriftlig oppgave.

Seminardagene vil til sammen utgjøre ca. 9 dager.

Godkjente arbeidskrav i andreårsemnet VERB2300, samt bestått alle øvrige studiepoenggivende emner fra 2. studieår.

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
• has a thorough understanding of the definitions of a smooth manifold and the tangent space
• knows the definitions and algebra of tensors and differential forms on a smooth manifold

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
• is able to implement and use a selection of numerical methods for solving ODEs and PDEs
• is able to give examples of smooth manifolds and prove their smooth manifold property from the definition
• is able to use the geometric concepts and tools associated with smooth manifolds in the analysis of mathematical problems within mathematics, physics and engineering

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
• is aware of the role of smooth manifolds as one of the most fundamental concepts in mathematics and physics

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

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. This will result in a report that should be 2000 - 4000 words of length plus figures.

Individuell skriftlig prosjekteksamen knyttet til praksis VERPRA21 Praksis i miljøterapeutisk arbeid, inntil 4000 ord.

Ved ikke bestått prosjekteksamen har studenten anledning til å levere omarbeidet versjon to (2) ganger, siden besvarelsen er tett knyttet opp til praksisgjennomføringen.

Alle hjelpemidler er tillatt så lenge regler for kildehenvisning følges

Gradert skala A-F

Skriftlig prosjekteksamen: Alle besvarelser vurderes av én sensor.  

Ekstern sensor benyttes regelmessig, og minimum ved hver tredje gjennomføring av emnet. Ved uttrekk av besvarelser til ekstern sensur skal uttrekket omfatte minimum 10 prosent av besvarelsene, men uansett ikke færre enn 5 besvarelser. Ved uttrekk skal ekstern sensors vurdering komme alle studentene til gode.

5 studiepoeng overlapp med VERPRA20 (full overlapp med del 2 prosjektoppgave i VERPRA20)