Paperback (ISBN-13: 9780898716344)
Page extent: 430 pages
Size: 247 x 174 mm
Special functions arise in many problems of pure and applied mathematics, mathematical statistics, physics, and engineering. This book provides an overview of numerical methods for computing special functions and discusses when to use these methods depending on the function and the range of parameters. It considers not only standard and simple parameter domains, but also describes methods valid for large and complex parameters. While its focus is on the computation of special functions, it is also suitable for general numerical analysis courses. The authors provide pseudoalgorithms to help students write their own algorithms, and also discuss other useful and efficient methods, such as methods for computing zeros of special functions, uniform asymptotic expansions and Pade approximations. It also includes specific algorithms for computing several special functions. Intended for researchers in applied mathematics, scientific computing, physics, engineering, statistics, and other scientific disciplines in which special functions are used as computational tools.
* Contains chapters describing basic methods, which are suitable for general
numerical courses * Includes references to recent literature on basic and
lesser-known methods for computing special functions * Introduces techniques
and methods that have previously only been described in scientific journals,
such as the numerical use of uniform asymptotic expansions
Contents
List of algorithms; Preface; 1. Introduction; Part I. Basic Methods: 2. Convergent and divergent series; 3. Chebyshev expansions; 4. Recurrence relations and continued fractions; 5. Quadrature methods; Part II. Further Tools and Methods: 6. Continued fractions; 7. Computation of the zeros of special functions; 8. Uniform asymptotic expansions; 9. Other methods; Part III. Related Topics and Examples: 10. Inversion of distribution functions; 11. Further examples; Part IV. Software: 12. Associated algorithms; Bibliography; Index.
Paperback (ISBN-13: 9780898716412)
Page extent: 456 pages
Size: 247 x 174 mm
The first in-depth, complete, and unified theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems: QR-like algorithms for dense problems and Krylov subspace methods for sparse problems. The author discusses the theory of the generic GR algorithm, including special cases (for example, QR, SR, HR), and the development of Krylov subspace methods. This book also addresses a generic Krylov process and the Arnoldi and various Lanczos algorithms, which are obtained as special cases. Theoretical and computational exercises guide students, step by step, to the results. Downloadable MATLAB programs, compiled by the author, are available on a supplementary Web site. Readers of this book are expected to be familiar with the basic ideas of linear algebra and to have had some experience with matrix computations. Ideal for graduate students, or as a reference book for researchers and users of eigenvalue codes.
* Studies generic examples of these two classes of algorithms, yet also
examines special cases * Contains many exercises, both theoretical and
computational, which will compel students to get stuck in and guide them
through processes step by step * A supplementary Web site is available,
containing a collection of downloadable MATLAB programs compiled by the
author
Contents
Preface; 1. Preliminary material; 2. Basic theory of Eigensystems; 3. Elimination; 4. Iteration; 5. Convergence; 6. The generalized Eigenvalue problem; 7. Inside the bulge; 8. Product Eigenvalue problems; 9. Krylov subspace methods; Bibliography; Index.
Series: Advances in Design and Control (No. 14)
Paperback (ISBN-13: 9780898716382)
Page extent: 370 pages
Size: 247 x 174 mm
A discussion of analysis and design techniques for linear feedback control systems using MATLABR software. By reducing the mathematics, increasing MATLAB working examples, and inserting short scripts and plots within the text, the authors have created a text suitable for almost any type of user. Suitable for beginners entering the field; for students who wish to bridge the gap between control theory and the use of MATLAB for control systems; and as a handy reference for practising engineers. The MATLAB companion package, CtrlLAB, allows readers to learn quickly while simply clicking through options with a mouse. Each chapter ends with a set of problems to help readers strengthen their understanding of the material. All example scripts within the book, as well as the CtrlLAB package, are freely downloadable from MATLAB Central, an open exchange for the MATLAB and SimulinkR community (www.mathworks.com/matlabcentral/index.shtml).
* Primarily intended as a reference for a first undergraduate course in
systems control, but also suitable for graduate students, researchers,
engineers, and scientists who are unfamiliar with control systems * Material
addressed includes model reduction issues, analysis, time domain, and control
designs. An entire chapter is also devoted to fractional-order controllers
* All example scripts within the book, as well as the CtrlLAB package,
are freely downloadable from MATLAB Central: a tool especially useful for
self-learners
Contents
Preface; 1. Introduction to feedback control; 2. Mathematical models of feedback control systems; 3. Analysis of Linear control systems; 4. Simulation analysis of nonlinear systems; 5. Model based controller design; 6. PID controller design; 7. Robust control systems design; 8. Fractional-order controller - an introduction; Appendix. CtrlLAB: a feedback control system analysis and design tool; Bibliography; Index of MATLAB functions; Index.
Series: CBMS-NSF Regional Conference Series in Applied Mathematics (No. 77)
Paperback (ISBN-13: 9780898716405)
Page extent: 250 pages
Size: 247 x 174 mm
Beginning with an overview of classical reservoir engineering and basic reservoir simulation methods, this book then progresses through a discussion of types of flows - single-phase, two-phase, black oil (three-phase), single phase with multi-components, compositional, and thermal. The author provides a thorough glossary of petroleum engineering terms and their units, along with basic flow and transport equations and their unusual features, and corresponding rock and fluid properties. The book also summarises the practical aspects of reservoir simulation, such as data gathering and analysis, and reservoir performance prediction. Suitable as a text for advanced undergraduate and first-year graduate students in geology, petroleum engineering, and applied mathematics; as a reference book; or as a handbook for practitioners in the oil industry. Prerequisites are calculus, basic physics, and some knowledge of partial differential equations and matrix algebra.
* Suitable as a student textbook, a reference book, or as a handbook for
practitioners in the oil industry * Useful to readers in various fields
such as geology, petroleum engineering, and applied mathematics * Provides
a thorough glossary of petroleum engineering terms and their units, along
with basic flow and transport equations and their unusual features, and
corresponding rock and fluid properties
Contents
List of figures; List of tables; List of notation; Preface; 1. Introduction; 2. A glossary of petroleum terms; 3. Single-phase flow and numerical solution; 4. Well modeling; 5. Two-phase flow and numerical solution; 6. The black oil model and numerical solution; 7. Transport of multicomponents in a fluid and numerical solution; 8. Compositional flow and numerical solution; 9. Nonisothermal flow and numerical solution; 10. Practical topics in reservoir