Assume that after preconditioning we are given a fixed point problem x = Lx + f (*) where L is a bounded linear operator which is not assumed to be symmetric and f is a given vector. The book discusses the convergence of Krylov subspace methods for solving fixed point problems (*), and focuses on the dynamical aspects of the iteration processes. For example, there are many similarities between the evolution of a Krylov subspace process and that of linear operator semigroups, in particular in the beginning of the iteration. A lifespan of an iteration might typically start with a fast but slowing phase. Such a behavior is sublinear in nature, and is essentially independent of whether the problem is singular or not. Then, for nonsingular problems, the iteration might run with a linear speed before a possible superlinear phase. All these phases are based on different mathematical mechanisms which the book outlines. The goal is to know how to precondition effectively, both in the case of "numerical linear algebra" (where one usually thinks of first fixing a finite dimensional problem to be solved) and in function spaces where the "preconditioning" corresponds to software which approximately solves the original problem.
This new edition introduces more problem-solving strategies and new conceptual and challenge problems. Also, each Chapter Review has been enhanced with Learning Goals to reinforce the mastery of concepts for students.
This laboratory manual contains 42 experiments for the standard sequence of topics in general, organic, and biological chemistry.
The book guides students through basic chemistry problem solving with engaging visuals and a focus on developing the math skills necessary to be successful in the course.
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Basic Chemistry
Basic Chemistry, Books a la Carte Edition
Essential Laboratory Manual for General, Organic and Biological Chemistry
The main objective in writing this text is to make the study of chemistry an engaging and a positive experience for students by relating the structure and behaviour of matter to real life.
The eText pages look exactly like the printed text, and include powerful interactive and customization functions. This is the product access code card for MasteringChemistry with Pearson eText and does not include the actual bound book.
Health, Environmental, and Green Chemistry Notes throughout the text relate chemistry chapters to real-life topics in health, the environment, and medicine that are interesting and motivating to students.