BYPE2000 Matematikk 2000 Emneplan

Dette emnet skal sammen med Matematikk 1000 gi studenten forståelse for matematiske begreper, problemstillinger og løsningsmetoder med sikte på anvendelser, spesielt innen ingeniørfaglige problemstillinger.

The following coursework is compulsory and must be approved before the student can sit the exam:

• Two milestone meetings of 1 hour each.

Ingen forkunnskapskrav.

Etter å ha gjennomført dette emnet har studenten følgende læringsutbytte, definert som kunnskap, ferdigheter og generell kompetanse:

Kunnskap

Studenten kan:

• gjøre rede for hvordan funksjoner kan approksimeres ved Taylorpolynom og potensrekker, forklare hva det vil si at rekker konvergerer, samt kunne derivere og integrere potensrekker leddvis
• beskrive Laplace-transformen, og vet om dens grunnleggende egenskaper
• beskrive og forklare hvordan tallfølger kan framkomme ved sampling (måling), ved bruk av formler, og som løsning av differenslikninger
• gjøre rede for interpolasjon av samplede data
• gjøre rede for partiell derivasjon, og bruke ulike grafiske måter å beskrive funksjoner av to variable
• beregne egenverdier og egenvektorer til matriser, og gi en geometrisk tolkning av disse størrelsene

Ferdigheter

Studenten kan:

• drøfte fordeler og ulemper ved å bruke interpolerende polynom, spliner og minste kvadraters metode for å interpolere samplede data
• drøfte feilskranker når tilnærmingspolynomer approksimerer funksjoner
• anvende enkle tester som for eksempel forholdstesten for å avgjøre konvergens av rekker
• tolke gradient og retningsderivert geometrisk
• anvende partiell derivasjon til å bestemme og klassifisere kritiske punkter til funksjoner av to variable
• bruke Laplace-transformen til å løse enkle ordinære differensiallikninger
• anvende egenverdimetoden til å løse lineære systemer av differensiallikninger med konstante koeffisienter

Generell kompetanse

Studenten kan

• vurdere resultater fra matematiske beregninger
• skrive presise forklaringer og begrunnelser til framgangsmåter, og demonstrere korrekt bruk av matematisk notasjon
• bruke matematiske metoder og verktøy som er relevante for eget fagfelt
• bruke matematikk til å kommunisere om ingeniørfaglige problemstillinger
• oversette et praktisk problem fra eget felt til matematisk form, så det kan løses analytisk eller numerisk

Fellesforelesning og øvingstimer. I øvingstimene arbeider studentene med oppgaver, dels individuelt, dels i grupper og får veiledning av faglærer.

Følgende arbeidskrav er obligatorisk og må være godkjent for å fremstille seg til eksamen:

• 3 av 4 oppgaver må leveres (ca. 2 timer per oppgave)

The bachelor's thesis is the final topic of the engineering education. It is a self-chosen task that is performed by students in a group. It will give students training in carrying out a large project independently and in using relevant methodology tools, and will be organised so that the students are able to use knowledge and skills from several fields.

The bachelor's thesis can be linked to assignments at OsloMet or be written in cooperation with business and industry or other institutions. It must be rooted in real engineering questions that are relevant to the chosen programme option and it can be related to design or contractor operations, orto a research or development project.

The bachelor's thesis is based on knowledge acquired through all five previous semesters.

Students must be registered in third year of the study and have completed at least 100 credits from the first and second years of study by 1st of October before they can register for the bachelor's thesis.

All three-semester courses must be passed.

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student:

• has good Professional knowledge in energy and environmental engineering issues
• has knowledge of different ways of addressing technical energy and environmental challenges
• demonstrates engineering insight with a holistic system perspective and various solution options
• has knowledge of accessible literature as well as ongoing research and development within the problem area
• can apply old and new knowledge to new knowledge and practical, holisticsolutions

Skills

The student is abel to:

• perform an engineering assignment given as a practical or research problem, in an independent and systematic way
• define problem, scope and Project goals and plan progress
• master appropriate methods and tools
• use relevant Professional theory and literature
• describe the task, analyze the results and discuss a conclusion
• communicate thesis, findings and conclusion clearly, both in writing and orally 

General competence

The student:

• masters working in teams With projct planning and execution
• demonstrates independence and initiative, creativity and innovation
• assesses technological solutions in a life-cycle/environmental, social and economic context
• analyzes and quality assures results and demonstrates the ability to reflect

Project work in groups. The groups should normally consist of three students. In exceptional cases when special reasons so dictate, students can be permitted to write the bachelor's thesis alone, based on application.

The assignment of bachelor's theses is based on the guidelines applicable to the faculty and the study programme. There will be a process from the end of the fourth semester until the assignment at the end of the fifth semester, when information  on guidelines is provided and selection of groups and tasks take place. A supervisor from the study programme will be appointed. An eventual external partner will  also normally provide guidance and follow-up.

The project work amounts to 500 hours per student and is concluded with a project report and oral presentation.

Students are expected to plan and execute the work in an independent manner and write timesheets. It shall be a written report in accordance with the faculty's procedures. Source reference must be performed correctly. Abstract must be written in English. Digital submission.

The assessment of learning outcomes will be based on the accomplishment and the report, an oral and visual presentation, including a poster presentation in plenary session and an oral individual examination.

1)    The report counts for 70%.

2)    The accomplishment and oral and visual presentation by the group, and the oral individual examination count for 30%.  

Part 1) of the exam: The exam results can be appealed.

Part 2) of the exam: The exam results cannot be appealed.

If the assessment of the written work is changed upon appeal, a new oral examination shall be arranged.

Both parts of the exam must be awarded grade E or better for the student to pass the course.