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Description of  Functional Linear Algebra

Linear algebra is an extremely versatile and useful subject. It rewards those who study it with powerful computational tools, lessons about how mathematical theory is built, examples for later study in other classes, and much more. Functional Linear Algebra is a unique text authored to address the need for a one-term linear algebra course when students have only had calculus. It does no assume students have had a proofs course. The text offers the following approach: Chapter 0 "Motivation" offers applications from engineering and the sciences to motivate students by revealing how linear algebra is used. Vector spaces over R. Complex vector spaces are briefly discussed in Appendix A.2.. More emphasis is placed on the idea of a linear function, which is used to motivate the study of matrices and their operations. This should seem natural to students after the central role of functions in calculus. Row reduction is moved further back in the semester and vector spaces are moved earlier to avoid an artificial feeling of separation between the computational and theoretical aspects of the course. As readers work through this book, it is important to understand the basic ideas, definitions, and computational skills. The best way to do this is to work through enough examples and problems to make sure the material is thoroughly grasped. The computational techniques used in this book can be done either by hand or using technology. This book specifically addresses how to use Mathematica, but feel free to use whichever technological tool best suits your needs. Table of Contents 0. Motivation 1. Vectors 2. Functions of Vectors 3. Vector Spaces 4. Diagonalization 5. Computational Vector Geometry Appendices A.1. Complex Numbers A.2. Mathematica A.3. Solutions to Odd Exercises Bibliography Index Author Biography Dr. Hannah Robbins is an associate professor of Mathematics at Roanoke College in Salem Virginia. Formerly a commutative algebraist, she now studies applications of linear algebra and assesses teaching practices in calculus. Outside the office she enjoys hiking and playing bluegrass bass.