Introduction to Numerical Analysis (NumIntro)
Course content
Numerical analysis is a field of mathematics that develops methods for obtaining solutions to problems, where it is not possible or appropriate to use explicit formulas. Such methods are often based on recursions, iterations, or more general algorithms. Numerical analysis has applications in all scientific fields where mathematical modeling is involved.
This course is both practical and theoretical. The student will work on understanding numerical algorithms and methods from a theoretical perspective. That means being able to prove the mathematical principles behind the numerical methods and being able to apply and adapt them to new situations.
In addition to the theoretical aspects, the course will include
implementing numerical methods on a computer using a programming
language. Here, the student must demonstrate that the theoretical
concepts can be translated into practice.
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Knowledge of:
Standard numerical methods for a selection of the following
topics:
- Nonlinear equations
- Systems of linear equations
- Eigenvalues
- Interpolation
- Differentiation and integration
- Differential equations
- Optimization and control
Basic programming in an imperative language, including:
- Procedures/functions
- Variables
- Recursion
- Statements, numerical expressions, scope, and more
Skills in a corresponding selection of the following:
- Numerical solution of nonlinear equations, systems of linear equations, and eigenvalue problems
- Approximation of functions, derivatives, and integrals
- Numerical solution of differential equations
- Numerical solution of small optimization problems
- Implementing and solving the above in an imperative programming language
Competencies to independently:
- Work with open-ended tasks where not all details are provided in advance
- Present mathematics in written form
- Use an imperative programming language to write and run small programs
- Explain the difference between “exact mathematics” and “numerical mathematics”
7 weeks of teaching consisting of lectures (4 hours per week) combined with theoretical and practical exercises (4 hours per week).
Lecture notes provided by the teacher.
Competences in mathematical analysis and linear algebra equivalent to those aquired in the courses Analyse 0 (An0), Analyse 1 (An1), Lineær algebra i de matematiske fag (LinAlgMat).
All participants must have a laptop for exercises, programming
tasks, and the exam.
The course is also aimed at bachelor's programmes in computer
science, the physical sciences, chemistry, and other bachelor's
and (as a foundational course) master's programmes which cover
the recommended academic qualifications.
- ECTS
- 7,5 ECTS
- Type of assessment
-
On-site written exam, 4 hours under invigilation
- Type of assessment details
- The final exam consists of a four-hour written exam.
In particular, the exam is divided in two parts of two hours each. - Examination prerequisites
-
It is necessary that two out of three assignments are approved and valid in order to participate in the final exam.
The assignments should be completed in groups of at most four students. - Aid
- Only certain aids allowed (see description below)
In the first part of the exam the students may use all written aid as well as a pocket calculator (lommeregner).
In the second part of the exam the students may use all aid (including a computer) except for internet and AI.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
- Re-exam
-
20 minutes oral exam on the entire curriculum without preparation.
If the assignments have not been approved before the ordinary exam, they must be completed on Absalon at the latest three weeks before the first exam day in the re-exam period.
Criteria for exam assessment
The student must satisfactorily demonstrate that they meet the course's learning objectives.
Single subject courses (day)
- Category
- Hours
- Lectures
- 28
- Preparation
- 68
- Exercises
- 28
- Study Groups
- 56
- Exam
- 26
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAB26001U
- ECTS
- 7,5 ECTS
- Programme level
- Bachelor
- Duration
-
1 block
- Placement
- Block 1
- Schedulegroup
-
C
- Capacity
- No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
- Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Giovanni Pantuso (2-6c75457266796d33707a336970)
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