Handbook

This is an applied mathematics course that builds on MATH2120 Mathematical Methods for Differential Equations. The course will present ways of solving the (usually partial) differential equations that arise in physical, biological, and engineering applications. Many of the methods covered, such as Fourier Transforms, also have applications beyond the solution … For more content click the Read More button below. The course begins by characterising different partial differential equations (PDEs), and exploring some methods of solution, such as similarity solutions and the method of characteristics. Integral transforms, including Fourier and Laplace transforms, are then investigated. These transforms are particularly useful for solving linear PDEs. Whilst complex contour integration is an intrinsic part of using these transforms, only brief references to complex variable methods will be made. The success of integral transforms naturally leads to the discussion of Green’s function and integral forms of the solution of PDEs. The power of Green’s functions can be observed in their use as the inverses of differential operators on both infinite and bounded domains. Finally, we will explore techniques to examine the asymptotic behaviour of functions. The course comprises of weekly lectures and tutorials.