Partial Differential Equations: An Introduction
This text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. Includes examples of inverse problems arising from improperly posed applications as well as exercises, many with answers.
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THE WAVE EQUATION
POTENTIAL THEORY AND FREDHOLM INTEGRAL
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a²u analysis analytic function apply approximations arbitrary assume bounded called Cauchy problem Chapter coefficients complex conclude condition consider constant continuously differentiable convergent defined DEFINITION denote derivatives determined Dirichlet problem disk domain ds(y eigenvalue equal example exists fact field Figure formula Fourier Fredholm given gives Green's harmonic heat equation Hence identically zero implies independent initial initial-boundary value problem integral equation interior inverse Laplace's equation layer potential linear maximum method normal Note obtained partial differential equations particular plane polynomial positive Proof prove respect satisfies scattering problem solution solve square integrable sufficiently Suppose tends to infinity tends to zero theorem theory uniformly unique valid vanish variables wave equation ди ду