MAT9170 – Spline Methods
Course description
Course content
This course gives an introduction to the theory and applications of piecewise polynomials represented by B-splines. In the first part the focus is on basic properties and algorithms of B-splines in one variable, and various approximation methods using these. Subsequently the theory and methods are extended to functions in multiple variables/dimensions, such as parametric curves and tensor products. In the last part of the course, the focus is on theoretical properties of B-splines, such as approximation properties and stability.
Learning outcome
After completing the course you know
- the basic properties and theory of B-splines
- how to implement basic algorithms for B-splines, such as evaluation, knot-insertion and interpolation
- how to use B-splines in practice, e.g. how to interpolate data in one or several variables
- how to present, on a scientific level, a short thesis on a chosen topic of relevance, selected in collaboration with the lecturer.
Admission to the course
PhD candidates from the Faculty of Mathematics and Natural Sciences at the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must?apply for a position as a visiting student?within a given deadline.
Recommended previous knowledge
- MAT1100 – Calculus
- MAT1110 – Calculus and Linear Algebra
- MAT1120 – Linear Algebra
- MAT-INF1100 – Modelling and Computations (discontinued)
- IN1000 – Introduction to Object-oriented Programming / IN1900 – Introduction to Programming with Scientific Applications
Overlapping courses
- 10 credits overlap with MAT-INF4170 – Spline Methods (continued).
- 10 credits overlap with MAT-INF9170 – Spline Methods (continued).
- 10 credits overlap with MAT4170 – Spline Methods.
Teaching
4 hours of lectures/exercises per week throughout the semester.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.
Examination
Final written exam or final oral exam, which counts 100 % towards the final grade.
The form of examination will be announced by the lecturer by 15 October/15 March for the autumn semester and the spring semester respectively.
This course has 4 mandatory assignments that must be approved before you can sit the final exam.
In addition, each PhD candidate is expected to give an oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer before you can sit the final exam.
It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT4170 – Spline Methods
Examination support material
No examination support material is allowed.
Language of examination
Courses taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.
Grading scale
Grades are awarded on a pass/fail scale. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.