Approximation techniques and variational principles represent vital tools for solving partial differential equations. This classic text introduces the reader to such solution methods at a level suitable for novices, before progressing through increasingly challenging problems. The book 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, how to use the finite element method for more complex problems, and how to ascertain error bounds. Applications to fluid mechanics and heat and mass transfer problems are emphasized throughout. With problem sets included, this book is ideal as both a resource for instructors of graduate-level courses on numerical analysis, and as a self-study guide for scientists and engineers.
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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.
Table of ContentsPreface to the classics edition; Preface; Acknowledgments; Part I. The Method of Weighted Residuals: 1. Introduction; 2. Boundary-value problems in heat and mass transfer; 3. Eigenvalue and initial-value problems in heat and mass transfer; 4. Applications to fluid mechanics; 5. Chemical reaction systems; 6. Convective instability problems; Part II. Variational Principles: 7. Introduction to variational principles; 8. Variational principles in fluid mechanics; 9. Variational principles for heat and mass transfer problems; 10. On the search for variational principles; 11. Convergence and error bounds; Author index; Subject index.