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The Method of Weighted Residuals and Variational Principles

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by Bruce A. Finlayson


2014 / xiv +412 pages / Softcover / ISBN: 978-1-611973-23-5 / List Price $99.00 / SIAM Member Price $69.30 / Order Code CL73

Keywords: variational principles, error bounds, Galerkin method, finite element method, transport problems, approximate solutions

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.

The Method of Weighted Residuals and Variational Principles

• describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles;
• illustrates how to use simple methods to find approximate solutions and how to use the finite element method for more complex problems; and
• provides detailed information on error bounds.

Problem sets make this book ideal for self-study or as a course text.

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.

About the Author
Bruce A. Finlayson is Rehnberg Professor Emeritus of Chemical Engineering at the University of Washington. He was a pioneer in the use of computers in chemical engineering education and has received numerous awards from the Chemical Engineering Division of the American Society for Engineering Education. He is the author of four books and a member of the National Academy of Engineering. He served as the President of the American Institute of Chemical Engineers in 2000.

Preface to the Classics Edition;
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.

ISBN: 9781611973235

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