This book is devoted to giving a modern view of iterative methods for solving linear and nonlinear equations, which are the basis for many, if not most, of the models of phenomena in science and engineering; their efficient numerical solution is critical to progress in these areas. The text provides motivating examples mainly from boundary value ......
And Related Problems of Mathematical Physics, Engineering, and Life Sciences
This book is the first to offer a systematic methodology for solving nonlinear ordinary differential equations (ODEs) using power series, specifically those arising in mathematical physics. It provides tools to eliminate the tedious manipulation of infinite series, enabling recursive computation of all terms. The authors also present a structured ......
This comprehensive book focuses on numerical methods for approximating solutions to partial differential equations. Intended as a broad survey of methods, the aim is to introduce readers to the central concepts of various families of discretizations and solution algorithm and lay the foundation needed to understand more advanced material, The book ......
Matrix eigenvalue problems arise in a wide variety of fields in science and engineering, so it is important to have reliable and efficient methods for solving them. Of the methods devised, bulge-chasing algorithms, such as the famous QR and QZ algorithms, are the most important. This book focuses on pole-swapping algorithms, a new class of methods ......
This is the only book devoted exclusively to Hessenberg and tridiagonal matrices. Hessenberg matrices are involved in Krylov methods for solving linear systems or computing eigenvalues and eigenvectors, in the QR algorithm for computing eigenvalues, and in many other areas of scientific computing (for instance, control theory). Matrices that are ......
A Promenade in Mathematical Proofs with Comprehensive Review of Proof Techniques is designed to support students as they advance their mathematical knowledge, bridging the gap from basic arithmetic and calculus to a deeper understanding of mathematical concepts through proof writing. It emphasizes the importance of being able to articulate ......
This book of worked-out examples not only accompanies Timothy M Hagle's earlier book Basic Math for Social Scientists: Concepts but also provides an informal refresher course in algebra sets, limits and continuity, differential calculus, multivariate functions, partial derivatives, integral calculus and matrix algebra. Problem sets are also provided so that readers can practice their grasp of standard mathematical procedures.
