Our purpose in writing this book is to provide the undergraduate student of engineering and science with a concise introduction to finite element methods one that will give a reader, equipped with little more than calculus, some matrix algebra, and ordinary differential equations, a clear idea of what the finite element method is, how it works, why it makes sense, and how to use it to solve problems of interest to him. We imposed on ourselves three constraints that we felt were of fundamental importance in designing a text of this type.
First, the treatment should not be burdened with technical details that are best appreciated by a more experienced reader. For instance, we feel that discussions of the many variauts of finite element methods, derailed aspects of computational schemes for implementing these methods, and numerous applications to problem areas in which the student may have little or no interest are not appropriate in a first course on the subject at this level. Here, we present the method in a form in which the truly salient features can be exposed and appreciated. We choose to relegate those other special topics to later, more advanced volumes.
Second, we did not want to produce either a cookbook or a handbook on finite elements. Although we do give ample coverage of the operational side of finite elements, we also seek to clarify and explain the basic ideas on which these methods are founded. Without these, the student has little foundation on which to build a deeper understanding of either these concepts or their generalizations and, equally important, cannot apply the methods intelligently to difficult problems.