Boundary integral equations (BIEs) have emerged as a powerful framework for modelling wave propagation, particularly in problems defined over unbounded or complex domains. By reformulating partial ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

The method of characteristics for solving first order quasilinear equations will be discussed. The three main types of linear second order partial differential equations will be considered: parabolic ...

Integral equations in various scientific theories and their relation to differential equations. Methods of solving linear problems with Hilbert Schmidt, Cauchy, and Wiener-Hopf type kernels; ...

Introduction to differential equations. Topics include methods of solutions for linear and non-linear first order differential equations, linear second order differential equations, higher order ...

Some equations are beautiful because they reveal unexpected relationships between different subjects. The Loewner differential equation, introduced by Charles Loewner in 1923, describes the time ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

APPM 5470, Methods of Applied Mathematics: Partial Differential and Integral Equations, Fall 2017 ...