This book should be accessible to students who have had a first course in matrix theory. The existence and uniqueness theorem of Chapter 4 requires the implicit function theorem, but we give a self-contained constructive proof ofthat theorem. The reader willing to accept the implicit function theorem can read the book without an advanced calculus background. Chapter 8 uses the Moore-Penrose pseudo-inverse, but is accessible to students who have facility with matrices. Exercises are placed at those points in the text where they are relevant. For U. S. universities, we intend for the book to be used at the senior undergraduate level or beginning graduate level. Chapter 2, which is on continued fractions, is not essential to the material of the remaining chapters, but is intimately related to the remaining material. Continued fractions provide closed form representations of the extreme solutions of some discrete matrix Riccati equations. Continued fractions solution methods for Riccati difference equations provide an approach analogous to series solution methods for linear differential equations. The book develops several topics which have not been available at this level. In particular, the material of the chapters on continued fractions (Chapter 2), symplectic systems (Chapter 3), and discrete variational theory (Chapter 4) summarize recent literature. Similarly, the material on transforming Riccati equations presented in Chapter 3 gives a self-contained unification of various forms of Riccati equations. Motivation for our approach to difference equations came from the work of Harris, Vaughan, Hartman, Reid, Patula, Hooker, Erbe & Van, and Bohner.
With two failed marriages and a broken soul, Amanda finally faces the demons that have chased her throughout her life in her tell-all, two-part memoir. As a survivor of domestic violence and sexual assault, Amanda bares her soul, addressing all of the normally secret emotions and struggles that come with trauma. In this two-part memoir series, Amanda shares the most intimate moments of her life that had led her to being the successful flight paramedic, mother, and wife she is today.
Arthur Conan Doyle was a British writer best known for his detective fiction featuring the character Sherlock Holmes. His works also include fantasy and science fiction, as well as plays, romances, non-fiction and historical novels. Filled with supernatural events, horrific scientific experiments, and bizarre events, “Tales of Mystery” is an excellent opportunity to discover another side of author’s ability to immerse and surprise.
Arthur Conan Doyle was a British writer best known for his detective fiction featuring the character Sherlock Holmes. His works also include fantasy and science fiction, as well as plays, romances, non-fiction and historical novels. This is a collection of medical and detective stories by Doyle, where he focused on the problems that present themselves to physicians and surgeons at the time.
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