Through many examples and real-world applications, Practical Linear Algebra: A Geometry Toolbox, Third Edition teaches undergraduate-level linear algebra in a comprehensive, geometric, and algorithmic way. Designed for a one-semester linear algebra course at the undergraduate level, the book gives instructors the option of tailoring the course for the primary interests: math, engineering, science, computer graphics, and geometric modeling.
New to the Third Edition
More exercises and applications
Coverage of singular value decomposition and its application to the pseudoinverse, principal components analysis, and image compression
More attention to eigen-analysis, including eigenfunctions and the Google matrix
Greater emphasis on orthogonal projections and matrix decompositions, which are tied to repeated themes such as the concept of least squares
To help students better visualize and understand the material, the authors introduce the fundamental concepts of linear algebra first in a two-dimensional setting and then revisit these concepts and others in a three-dimensional setting. They also discuss higher dimensions in various real-life applications. Triangles, polygons, conics, and curves are introduced as central applications of linear algebra.
Instead of using the standard theorem-proof approach, the text presents many examples and instructional illustrations to help students develop a robust, intuitive understanding of the underlying concepts. The authors' website also offers the illustrations for download and includes Mathematica (R) code and other ancillary materials.
Rezensionen / Stimmen
Praise for the Second Edition:"... quite appropriate for students in engineering and computer graphics as well as in mathematics. It is well written and the examples are carefully chosen to motivate or exemplify the topic at hand. ... Recommended."
-J.R. Burke, CHOICE, September 2005
"I picked up this book with the thought, 'oh, another linear algebra text.' I was pleasantly surprised, upon examination, that it is not just another one. The standard linear algebra material is presented with good motivating stories, illustrations, and examples."
-CMS Notes, February 2006
"[The] mixture of linear algebra, geometry, and numerical aspects is very interesting and will probably stimulate the students."
-Bulletin of the Belgian Mathematical Society, December 2005
"Teaching computer graphics and mathematics in the study program Digital Media, I have found Practical Linear Algebra to be precisely the kind of book I've long been looking for. It covers all topics that are vital for computer graphics, even gives lots of applications in that field, including for instance PostScript, and does so in a very practical but nonetheless rigorous manner. I find many elements of my own teaching in this book, including the hand-made style of drawings (rendering them more 'hands-on'), using a geometric shape to illustrate the action of a 2x2 matrix, and deriving the determinant from the computation of areas and volumes instead of plainly presenting a formula. I have recommended this book strongly to all students in my first-year courses and will continue to do so."
-Joern Loviscach, University of Applied Sciences Bremen
"I was impressed with the applications, especially those related to computer graphics. ... I think some faculty will be interested in using the book because the geometric descriptions and applications are very nice."
-Linda Patton, Cal Poly San Luis Obispo
"I just purchased your book ... and I immediately fell in love with it. I love the nice illustrations and diagrams, which are very helpful in promoting an intuitive understanding of every concept. I am a clinician investigator at the National Institutes of Health who is conducting MRI research of the heart. My main interest is finite deformation of the heart muscle structures; however, since I do not have an engineering background, I have been looking for a nice textbook on linear algebra."
-Hiroshi Ashikaga, National Institutes of Health
"After having finished your book today, I agree completely with the very favorable reviews that I saw on the Internet. It was an enlightening experience to brush up on my old university math with this book. The 'sketchy' way of explaining things sure worked for me."
-Anneke Sicherer-Roetman, Maritime Research Institute Netherlands
"... it's done a world of wonder for me, as I need to review my linear algebra to prepare for studying computer graphics. I really can't thank you enough."
-Daniel Kurtz, Northeastern University
"Practical Linear Algebra is great. I write software for the image analysis of medical images where in several occasions I have had to deal with eigen things and [others]. I have been using your book as a valuable reference to refresh and understand these concepts that I studied when I was a student."
-Diego Bordegari
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Illustrationen
492 s/w Abbildungen
492 Illustrations, black and white
Maße
Höhe: 235 mm
Breite: 191 mm
Gewicht
ISBN-13
978-1-4665-7956-9 (9781466579569)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Farin, Gerald; Hansford, Dianne
Descartes' Discovery. Here and There: Points and Vectors in 2D. Lining Up: 2D Lines. Changing Shapes: Linear Maps in 2D. 2 x 2 Linear Systems. Moving Things Around: Affine Maps in 2D. Eigen Things. 3D Geometry. Linear Maps in 3D. Affine Maps in 3D. Interactions in 3D. Gauss for Linear Systems. Alternative System Solvers. General Linear Spaces. Eigen Things Revisited. The Singular Value Decomposition. Breaking It Up: Triangles. Putting Lines Together: Polylines and Polygons. Conics. Curves. Appendices. Bibliography. Index.
