The hyperbolization theorem for Haken 3-manifolds. The book is written to be accessible to second-year graduate students. Hubbard has written a beautiful set of books. We all look forward to the sequel. This second volume provides proofs of the first two of Thurston's four theorems: the classification of homeomorphisms of surfaces and the topological characterization of rational maps.
Each says that either a topological problem has a natural geometry, or there is an understandable obstruction. Thurston proceeds to show that if there is no fixed point, then some system of simple closed curves is an obstruction to finding a solution. He carried out this task with great patience and care and he did a remarkable job. In Chapter 5 the author attacks the interesting and difficult problem of comparing the numerical work required to solve large elliptic problems by his SOR-like AGA method, with the numerical work required using newer computational methods, such as Krylov subspace methods and GMRES.
Indeed, for some problems, he found that the SOR-like methods were superior to Krylov subspace methods by several orders of magnitude.
Featured reader comments Volume 1 of Teichmuller theory has been a joy to read. Reader comments for Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach Quick links These links will take you to a brief description of the book; for more information, click on the book cover or title.
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Showing Average rating 0. Rating details. All Languages. More filters. Sort order. Linear Algebra: A Geometric Approach, Second Edition , presents the standard computational aspects of linear algebra and includes a variety of intriguing interesting applications that would be interesting to motivate science and engineering students, as well as help mathematics students make t Students - Buy or Rent.
Read and study old-school with our bound texts. Rent 3 months. Rent 4 months. Rent 6 months. Rent 1 year. Home Features New to This Edition. Geometry is introduced early , using vector algebra to do analytic geometry in the first section and dot product in the second. Concepts and understanding is emphasized, doing proofs in text and providing plenty of exercises. To aid the student in adjusting to the mathematical rigor, blue boxes are provided which discuss matters of logic and proof technique or advice on formulating problem-solving strategies.
Rotations, reflections, and projections are used as a first brush with the notion of linear transformation when introducing matrix multiplication. Linear transformations are then treated in concert with the discussion of projections.
Thus, the change-of-basis formula is motivated by starting with a coordinate system in which a geometrically defined linear transformation is clearly understood and asking for its standard matrix.
Orthogonal complements are emphasized, with their role in finding a homogenous system of linear equations that defines a given subspace of Rn. New to This Edition. New to Chapter 3, Vector Spaces: streamlined treatment of four fundamental subspaces and clarified coverage of linear independence and basis. Updated and reorganized Chapters 4, Projections and Linear Transformations, and 5, Determinants with improved clarity in the coverage of Change of Basis and the geometric material.
Stronger emphasis throughout on key concepts and understanding, through new proofs and a variety of text exercises. New Blue Boxes , integrated throughout the text, discuss matters of logic and proof techniques or advice on formulating problem-solving strategies to aid the student in adjusting to the mathematical rigor. Digital Options. Table of Contents. Chapter 1. Vectors and Matrices 1. Vectors 2. Dot Product 3. Hyperplanes in Rn 4.
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