Mathematical Analysis, Geometry, Numerics and Systems
Source: https://www.utwente.nl/en/education/master/programmes/applied-mathematics/specialisation/mathematical-analysis-geometry-numerics-systems/ Parent: https://www.utwente.nl/en/education/master/programmes/applied-mathematics/
Master the mathematics behind dynamical systems, focusing on understanding, predicting, and controlling changes in physical and technical systems over time.
How does blood flow through the human body? What does it take for a car to run independently? And how does the atmosphere change due to climate change? These questions all have one thing in common: they deal with dynamical systems: systems involving changes in variables that unfold over time. The specialisation in Mathematical Analysis, Geometry, Numerics and Systems focuses on fundamental aspects of dynamical phenomena, and computational and control aspects thereof. You will become an expert in developing and applying mathematical tools for solving problems that arise in physical and technical systems.
In this specialisation, we focus on mathematical methods for systems governed by natural laws, modelled with (partial) differential equations. This involves analysing and simulating system behaviour, solving inverse problems, and optimal control—all of which require both rigorous analysis of (P)DEs and efficient computational methods to maintain accuracy and speed.
Matthias Schlottbom, Chair of the Mathematics of Computational Science group.
What is Mathematical Analysis, Geometry, Numerics and Systems?
In this specialisation, you will delve deeper into topics in the area of dynamical systems, numerical analysis and scientific computing, and systems and control. This will enable you to become a true mathematical model expert, able to design new, robust mathematical models and apply current ones to make processes more comprehensible, and predict or improve the behaviour of physical and technical systems.
Examples of courses you (can) follow during this specialisation:
- How can you accurately simulate complex phenomena governed by partial differential equations, like fluid dynamics or heat transfer, using effective numerical methods across diverse applications in engineering and physics? In the course Numerical Techniques for Partial Differential Equations, you will explore these questions and gain practical skills in implementing advanced numerical methods to tackle real-world problems.
- How can mathematical frameworks be applied to analyze and design complex systems in engineering and science? What theoretical concepts underpin the control of dynamic systems, ensuring stability and performance? In the course Systems and Control, you will delve into these fundamental questions, exploring advanced theories and methodologies from mathematics that are essential for understanding system behavior and control strategies in various applications.
- Laws of nature are often formulated in terms of partial differential equations (PDEs). Understanding nature is thus intimately related to the mathematical analysis of PDEs: Does a solution of the equation exists, and if, what are its properties? In the course Partial Differential Equations, you employ modern, deep mathematical tools to answer such questions for linear and non-linear PDEs.
You will learn how to outline practical problems and pinpoint their abstraction. In fact, many systems can ultimately be brought back to the same mathematical core. So the great thing about these models is that you can apply them in totally different contexts. Omitting what’s context-specific will allow you to create abstract models that can be objectively applied in any given context. Application areas include neuroscience, advanced tracking, vehicle control, fluid dynamics and optics. You might focus on deep brain stimulation in countering Parkinson’s disease, or designing control algorithms for self-driving cars, to name just a few of the many examples.
What will you learn?
As a graduate of this Master's and this specialisation, you have acquired specific, scientific knowledge and skills and values, which you can put to good use in your future job.
Knowledge
After completing this Master’s specialisation, you:
- have a comprehensive understanding of state-of-the-art numerical methods for solving a wide range of problems in science and engineering, including large linear systems of equations, control systems, ordinary and partial differential equations, as well as advanced techniques such as model order reduction;
- have a profound understanding of the principles underlying linear dynamical systems and their representations. You will explore key concepts such as system behaviour, stability, and control techniques, along with the mathematical frameworks used to analyse and design these systems, preparing you for applications in engineering and science;
- have a deep understanding of functional analysis and the analysis of partial differential equations (PDEs). You will study essential concepts such as Banach and Hilbert spaces, linear operators, and the existence and uniqueness of solutions to PDEs, equipping you with theoretical foundations for tackling complex problems in mathematics and related fields.
Skills
After successfully finishing this Master’s specialisation, you will have:
- the ability to formulate and analyse dynamical systems using differential equations and state-space methods;
- expertise in designing feedback and optimal control strategies to regulate system behaviour in various applications;
- proficiency in applying and implementing computational algorithms to solve large-scale mathematical problems and simulate complex systems.
Values
After completing this Master’s specialisation, you will:
- understand the ethical implications of mathematical models and control systems, ensuring their safe and responsible use in society.
- recognise the importance of developing efficient and sustainable solutions to address environmental challenges through mathematical analysis and modelling.
- value interdisciplinary collaboration and the societal impact of applied mathematics in solving real-world problems, such as those in the energy transition and healthcare.
Other master’s and specialisations
Is this specialisation not exactly what you’re looking for? Maybe one of the other specialisations suits you better. Or find out more about these other related Master’s:
- Master’s in Applied Physics - specialisation Applied Nanophotonics or Physics of Fluids
- Master’s in Computer Science
- Master's in Civil Engineering - specialisation Water Engineering & Management
- Master's in Mechanical Engineering - specialisation Aeronautics
- Master's in Robotics - specialisation Mechatronics & Physical AI