Recommendation of Textbooks

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

A. P. S. Selvadurai

Springer, 2000

ISBN 3540672842, 9783540672845

698 p

There is a free copy of part of this book online. One can serch it.

In this book there are lots of wonderful examples in solid mechanics that can be solved by using "dark-age" method. One can learn both basic concepts and mathematical skills from this book. And one can also use it as a reference book.

Abstract of this book

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.