Partial Differential Equations
Bachelor's degree
In Oxford
Description
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Type
Bachelor's degree
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Location
Oxford
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Start date
Different dates available
Partial differential equations (PDEs) are at the heart of many scientific advances. The behaviour of every material object in nature, with time scales ranging from picoseconds to millennia and length scales ranging from sub-atomic to astronomical, can be modelled by deterministic and stochastic PDEs or by equations with similar features. Indeed, many subjects revolve entirely around underlying PDEs, including:The role of PDEs within mathematics, especially non-linear analysis, geometry, topology, stochastic analysis, numerical analysis, and applied mathematics, and in other sciences (such as physics, chemistry, life sciences, climate modelling/prediction, materials science, engineering, and finance) is thus fundamental and is becoming increasingly significant.
Facilities
Location
Start date
Start date
Reviews
Subjects
- IT
- Mathematics
- GCSE Mathematics
Course programme
At the same time, the demands of applications have led to important developments in the analysis of PDEs, which have in turn proved valuable for further different applications.
- Fluid dynamics: the Euler equations and the Navier-Stokes equations
- Electrodynamics, optics and electric circuits: Maxwell’s equations
- Non-equilibrium statistical mechanics: the Boltzmann equation
- Quantum mechanics: the Schrödinger equation
- Cosmology: the Einstein equations of general relativity
A sizeable yearly cohort will allow the CDT to create new training mechanisms, so that you will learn theory, analysis, and applications in a variety of fields in a coherent manner with a natural progression, by-passing a traditionally separate 'pure' or 'applied' approach to learning.
You will undertake a four-year programme with the first year consisting of a set of intensive courses focusing on the analysis and applications of PDEs. The first year also includes two 10-week mini-projects, a spring retreat and a summer school. There will be annual review of your progress drawing on indicators such as attendance, mini-project and course results at the end of your first year; by submission of a written report and oral examination at the end of your second and third years.
It is expected that those successfully completing the training programme will go on to undertake further research in academia/industry or work in industry.
Partial Differential Equations