Partial Differential Equations in Mechanics 2: The Biharmonic Equation, Poisson’s Equation

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This two-volume work mainly addresses undergraduate and gra- duate students in the engineering sciences and applied ma- thematics. Hence it focuses on partial differential equati- ons with a strong emphasis on illustrating important appli- cations in mechanics. The presentation considers the general derivation of partial differential equations and the formu- lation of consistent boundary and initial conditions requi- red to develop well-posed mathematical statements of pro- blems in mechanics. The worked examples within the text and problem sets at the end of each chapter highlight enginee- ring applications. The mathematical developments include a complete discussion of uniqueness theorems and, where rele- vant, a discussion of maximum and miniumum principles. The primary aim of these volumes is to guide the student to pose and model engineering problems, in a mathematically correct manner, within the context of the theory of partial differential equations in mechanics.