Thursday, May 23, 2013

Linear Algebra with Applications 5th Edition, Bretscher

Linear Algebra with Applications 5th Edition PDF Download Ebook. Otto Bretscher emphasizes linear transformations as a unifying theme. This elegant textbook combines a user-friendly presentation with straightforward, lucid language to clarify and organize the many techniques and applications of linear algebra. Exercises and examples make up the heart of the text, with abstract exposition kept to a minimum.

Extensive problem sets keep students involved in the material, while genuine applications for a broad range of sciences prepares them for the methods and models of contemporary scientists. In addition, the wealth and variety of exercise sets enable instructors to design a course to best suit the goals and needs of their students. This revision reflects careful review and appropriate changes to the wording of each idea, while preserving the content structure of the previous edition.

Linear transformations are introduced early in the text to make the discussion of matrix operations more meaningful and easier to navigate. Visualization and geometrical interpretation are emphasized extensively throughout the text. An abundance of problems, exercises, and applications help students assess their understanding and master the material.

Abstract concepts are introduced gradually throughout the text. Major ideas are carefully developed at various levels of generality before the student is introduced to abstract vector spaces. Discrete and continuous dynamical systems are used as a motivation for eigenvectors and as a unifying theme thereafter. Fifty to sixty True/False questions conclude every chapter, testing conceptual understanding and encouraging students to read the text.

Historical problems from ancient Chinese, Indian, Arabic, and early European sources add diversity to the selection of exercises. Rotations, reflections, projections, and shears are used throughout to illustrate new ideas. Multiple perspectives on the kernel of a matrix are presented, with a stronger emphasis on the relations among the columns.

Commutative diagrams enhance students' conceptual understanding of the matrix of a linear transformation. These diagrams enable students to visualize the relations between linear transformations. A more conceptual approach to the QR factorization is presented, in terms of a change-of-basis.

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