The Laplacian is a differential operator that plays a crucial role in various fields such as physics, mathematics, and engineering, often used to describe the rate at which a quantity diffuses through space. It is defined as the divergence of the gradient of a function, and is central to equations governing phenomena like heat conduction, wave propagation, and quantum mechanics.
Conformal mapping is a mathematical technique used in complex analysis to transform one domain into another while preserving angles and the shapes of infinitesimally small figures. It is instrumental in solving problems in physics and engineering, particularly in areas like fluid dynamics and electromagnetic theory, where it simplifies complex boundary conditions.
Static potential problems involve determining the electric or gravitational potential in a region where the sources are fixed and do not change over time. These problems are typically solved using techniques from electrostatics or gravitation, often involving boundary conditions and the Laplace or Poisson equations.