Faglige nøgleord: Math, Mathematics, Modeling, Computing, Engineering, Differential equations, PDE, Functional analysis, Existence & Uniqueness & Stability, Finite Element Method
Oplæg tilgængeligt på: Dansk og engelsk
In the realm of mathematics, the rules that apply are whichever we decide. We can choose rules that mimic what we observe in the real world, and build models with incredible predictive powers. We can also tweak or remove rules to arrive at curious, surprising, even counter-intuitive conclusions.
In this presentation I want to share my obsession with the aforementioned beauty and the weirdness of mathematics. I will relate it to the particular field that I work with, which is differential equations. Fascinating oddities are unveiled through critical questions like “How many solutions does an equation have?”, “How can we know that an equation even has any solutions?”, “If we can’t solve an equation exactly, how close can we at last get?”, etc. These beg the question “What does it actually mean to solve an equation?”
To make things more tangible and engaging, I want to focus on:
- Where differential equations are used to model real world problems today.
- How solutions to these equations are being utilized by technology that we all use in our daily lives.
- How the solutions are approximated in practice, using numerical computer algorithms.
I hope to inspire a fascination for Mathematical Modeling and Computation, and give an understanding of the importance that it plays in all of science and engineering