Numerical Analysis: Simulation Tools

This course offers you the opportunity to apply your mathematical and programming skills to complex problems inspired by real industrial applications. Working in small teams, you will engage with simulation inspired by industrial challenges, focusing on mechanical systems and advanced numerical methods.

During the course, you will learn how to model and solve problems involving differential equations with discontinuities, algebraic constraints, and large nonlinear systems. You will also explore how these mathematical approaches are implemented in commercial simulation

Topics include

• multistage methods and SUNDIALS implementation
• methods for rigid and non-rigid problems
• highfrequency problems
• differentialalgebraic equations and forced conditions
• Discontinuous differential equations and related modelling assumptions.

The course is alternativecompulsory within the Master’s Programme in Mathematics with a specialisation in Numerical Analysis. It may be taken as an elective within the Master’s Programme in Computational Science (Geoscience and Scientific Computing), and it is open as an elective course in mathematics for Bachelor’s students who have the necessary background. The course is also offered as a standalone course.

Teaching is organised around three major simulation projects. The course begins with lectures introducing the theoretical background and algorithms relevant to each project. You will then collaborate in teams to develop computational solutions, document your modelling decisions, and present your results.

At the end of the course, you will submit a final report and give an oral presentation, which constitute the main forms of assessment. The course promotes independent reasoning, collaborative problemsolving, and clear communication—abilities that are highly valued in both academic and industrial environments.

By completing this course, you will be well prepared for work in simulation and modelling in both research and industry. The competencies you gain are highly relevant in engineering, applied mathematics, and computational science. You will be able to critically evaluate simulation tools, contribute as a specialist or consultant in simulationdriven contexts, and continue with advanced studies or research in numerical analysis and scientific computing.

Prerequisites

30 ECTS credits in mathematics and additional 60 ECTS credits in mathematics and/or physics including knowledge corresponding to the courses NUMN32 Numerical Methods for Differential Equations, 7.5 credits and NUMA01 Computational Programming with Python, 7.5 credits. English 6 /English course B.

Selection criteria

Seats are allocated according to: ECTS (HPAV): 100 %.

Tuition fees for non-EU/EEA citizens

Citizens of countries outside:

• The European Union (EU)
• The European Economic Area (EEA) and
• Switzerland

are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.

Tuition fees, payments and exemptions

Full programme/course tuition fee: SEK 21,250
First payment: SEK 21,250

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Note that you may also need to pay an application fee, or provide proof of exemption.

Application fee

No tuition fees for citizens of the EU, EEA and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.