👉 Lap math, short for Laplace's equation, is a fundamental partial differential equation used in various fields such as physics, engineering, and mathematics to describe phenomena involving potential fields, like electric or gravitational fields. It is expressed as ∇²φ = 0, where φ represents the potential function and ∇² is the Laplacian operator. The equation states that the sum of the second partial derivatives of φ with respect to each spatial variable is zero, implying that the potential varies smoothly without any sources or sinks. In practical terms, this means that if you know the boundary conditions on a domain, the solution to Laplace's equation within that domain is unique and can be determined by applying methods like separation of variables or Fourier series. Laplace's equation is crucial for understanding steady-state processes and solving problems in electrostatics, fluid dynamics, and heat conduction.
