This text can be used for two quite different purposes. It can be used as a reference book for the PDElPROTRAN user- who wishes to know more about the methods employed by PDE/PROTRAN Edition 1 (or its predecessor, TWODEPEP) in solving two-dimensional partial differential equations. However, because PDE/PROTRAN solves such a wide class of problems, an outline of the algorithms contained in PDElPROTRAN is also quite suitable as a text for an introductory graduate level finite element course. Algorithms which solve elliptic, parabolic, hyperbolic, and eigenvalue partial differential equation...

This book presents methods for the computational solution of some important problems of linear algebra: linear systems, linear least squares problems, eigenvalue problems, and linear programming problems. The book also includes a chapter on the fast Fourier transform and a very practical introduction to the solution of linear algebra problems on modern supercomputers.The book contains the relevant theory for most of the methods employed. It also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs for solving...

This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A.The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects...

This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A.The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects...

In this revised and expanded collection of essays on origins, mathematician Granville Sewell looks at the big bang, the fine-tuning of the laws of physics, and (especially) the evolution of life. Sewell explains why evolution is a fundamentally different and much more difficult problem than others solved by science, and why increasing numbers of scientists are now recognizing what has long been obvious to the layman, that there is no explanation possible without design. This book summarizes many of the traditional arguments for intelligent design, but presents some powerful new arguments as...

In Christianity for Doubters, mathematician Granville Sewell looks at a series of issues that cause Christians to doubt. The first two chapters effectively counter the widely believed idea that science can explain how we got here without design. The remaining chapters examine, from a non-fundamentalist point of view, some of the theological issues that educated Christians struggle with, including problems with the Bible, the idea of a resurrection, and the problem of pain. Although these theological problems are more difficult, the author shows that some of the most important insights into...