Complex Exponential Method for Solving Partial Differential Equations

For constant-coefficient linear partial differential equations solvable by separation of variables, an alternative solution method is proposed. The method employs complex exponential functions to find exact analytical solutions. Examples include the heat conduction equation, homogenous and non-homogenous wave equations, and the beam vibration equation. The method can be effectively used for partial differential equations (PDEs) whose solutions can be expressed as a product of harmonic and/or exponential type series.