Classical complex analysis lies just under the surface of many techniques for analysing differential equations. This is evident in the study of Laplace transforms, Fourier analysis, power series methods, analysis of singular points, and many other places. The purpose of this project will be to focus on the interplay between these subjects and to find new connections, if possible. Several topics will be studied deeply, including the use of complex analytic techniques to invert Laplace and Fourier transforms. Analysis of certain PDEs on particular domains of the complex plane will also be studied.
Preet Patel is an undergraduate student at Monash University, studying a Bachelor of Science, majoring in mathematics, and a Bachelor of Engineering, majoring in electrical and computer systems. He has strong interests in Euclidean geometry and differential equations as problems in these fields require creativity to solve and can often be tackled in many ways. He works with several schools and students to teach Olympiad Mathematics, a domain in which he previously contended as a high-school student. He also enjoys programming and creating algorithms to solve problems or simplify everyday tasks. Outside of STEM, Preet undertakes a Diploma of Languages majoring in Mandarin, and enjoys hiking around Victoria.