Program Overview

Introduction to the Numerical Analysis Program

The Numerical Analysis program is designed to provide students with a comprehensive understanding of numerical methods and their applications in various fields. The program builds on the knowledge obtained from previous modules, including Linear Algebra with Applications, Analysis 1, and Probability Theory.

Program Details

Recommended Prerequisite for Participation

The module builds on knowledge obtained by the modules Linear Algebra with Applications, Analysis 1, and Probability Theory from the BSc in Mathematics or similar.

Content, Progress, and Pedagogy of the Module

Learning Objectives

Knowledge

• Have knowledge of floating point arithmetic, including the international standards for floating point arithmetic
• Have knowledge of error analysis and stability of numerical algorithms
• Have knowledge of polynomial interpolation and its application to the derivation of numerical algorithms
• Have knowledge of basic results in approximation theory
• Have knowledge of methods for finding zeroes of functions
• Have knowledge of numerical linear algebra, in particular algorithms adapted to large sparse systems of linear equations
• Have knowledge of methods for numerical differentiation, including spectral methods
• Have knowledge of methods for numerical integration, including Gaussian quadrature
• Have knowledge of numerical solution methods for ordinary differential equations, including spectral methods
• Have knowledge of some probabilistic methods in numerical analysis, including Monte-Carlo methods

Skills

• Can implement basic numerical algorithms in different computer architectures
• Can choose appropriate numerical methods to solve a given class of problems

Competences

• Can evaluate the appropriateness of a given numerical method for solving a class of problems
• Are aware of the limitations of numerical methods to solve a class of problems

Extent and Expected Workload

This is a 5 ECTS project module, and the workload is expected to be 150 hours for the student.

Exam

Exams

• Name of exam: Numerical Analysis
• Type of exam: Oral exam
• ECTS: 5
• Assessment: Passed/Not Passed
• Type of grading: Internal examination
• Criteria of assessment: The criteria of assessment are stated in the Examination Policies and Procedures

Facts about the Module

• Danish title: Numerisk analyse
• Module code: K-MAT1-NUANL
• Module type: Course
• Duration: 1 semester
• Semester: Autumn
• ECTS: 5
• Language of instruction: Danish
• Empty-place Scheme: Yes
• Location of the lecture: Campus Aalborg
• Responsible for the module: Henrik Garde, Arne Jensen
• Used in:
  • Master in Mathematics, 2020
  • Master in Mathematical Economics, 2020
  • Master of Science (MSc) in Mathematics 2022
  • Master of Science (MSc) in Engineering (Mathematical Engineering) 2022
  • Master of Science (MSc) in Mathematics-Economics 2022

Organisation

• Study Board: Study Board of Mathematical Sciences
• Department: Department of Mathematical Sciences
• Faculty: The Faculty of Engineering and Science