Unified transform lab

Yale-NUS College



The unified transform lab is an undergraduate research laboratory, directed by Assistant Professor Dave Smith, located at Yale-NUS College. We seek to answer questions in applied mathematics, often related to waves and other physical systems.

Undergraduate research

Undergraduates can undertake research in applied mathematics at a variety of levels. Applied mathematics involves developing, testing and proving hypotheses about mathematical models of the real world. Some of this work requires you to have completed some (or many!) mathematics modules, but some is accessible if you can do a little computer programming. Students have been members of the unified transform lab as early as the summer after their first year of enrollment at Yale-NUS College.

Get involved

If you are an undergraduate student at Yale-NUS College and you are interested in getting involved in research in applied mathematics, then you should read more about the research we do and the specific projects we offer. You can also peruse the projects completed in the lab to see what kinds of topics others have been working on. Capstone students from the MCS major are always welcome. There are also some funded research opportunities during the summer break and during the semester. Look on NSWS or contact Dave for more information about current and upcoming opportunities.


We do research using a wide array of mathematical techniques, focussed on developments and applications of the unified transform method. Applications are usually in the field of linear evolution partial differential equations in 1 space and 1 time dimension, of high spatial order. This setting can be used to model water waves, data in networks, distribution of heat in solids and deformation of a flexible beam. Development of the method can involve any combination of real analysis, complex analysis, asymptotic analysis, fractional calculus, linear algebra, and computer programming.

You can find a longer introduction to what applied mathematics means and the research we do on the research page. We also maintain details of completed projects, and some open projects available for students.

Recent publications

Accepted: The Airy equation with nonlocal conditions

Published: Fokas diagonalization of piecewise constant coefficient linear differential operators on finite intervals and networks

Published: Linear evolution equations on the half line with dynamic boundary conditions