NMAB26001U Introduction to Numerical Analysis (NumIntro)

Volume 2026/2027
Education

Bachelor's programme in Natural Resources
Bachelor's programme in Animal Science
Bachelor's programme in Actuarial Mathematics
Bachelor's programme in Mathematics
Bachelor's programme in Mathematics-Economics

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. 

Learning Outcome

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”

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).
7 weeks of teaching consisting of lectures (4 hours per week) combined with theoretical and practical exercises (4 hours per week).
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.
  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 68
  • Exercises
  • 28
  • Study Groups
  • 56
  • Exam
  • 26
  • Total
  • 206
Continuous feedback during the course of the semester
Credit
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 assesment

The student must satisfactorily demonstrate that they meet the course's learning objectives.