The method of weighted residuals and variational principles
Bruce A. Finlayson
SIAM-Society for Industrial and Applied Mathematics
This classic book covers the solution of differential equations in science and engineering in such as way as to provide an introduction for novices before progressing toward increasingly more difficult problems.<p> <p> <i>The Method of Weighted Residuals and Variational Principles</i> describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles. The book also illustrates how to use simple methods to find approximate solutions, shows how to use the finite element method for more complex problems, and provides detailed information on error bounds.<p>  <p> Problem sets make this book ideal for self-study or as a course text.<p> <p> <b>Audience:</b> Engineers and scientists who need to solve differential equations and want to have a deeper understanding of some of the available methods, particularly in fluid mechanics, will find this book useful. Instructors of graduate-level courses that cover approximate and numerical solutions can use it as a textbook.<p> <p> <b>Contents:</b> Preface to the Classics Edition; Preface; Acknowledgments; Part I: The Method of Weighted Residuals; Chapter 1: Introduction; Chapter 2: Boundary-Value Problems in Heat and Mass Transfer; Chapter 3: Eigenvalue and Initial-Value Problems in Heat and Mass Transfer; Chapter 4: Applications to Fluid Mechanics; Chapter 5: Chemical Reaction Systems; Chapter 6: Convective Instability Problems; Part II: Variational Principles; Chapter 7: Introduction to Variational Principles; Chapter 8: Variational Principles in Fluid Mechanics; Chapter 9: Variational Principles for Heat and Mass Transfer Problems; Chapter 10: On the Search for Variational Principles; Chapter 11: Convergence and Error Bounds; Author Index; Subject Index