Publisher's Synopsis
Linear Algebra with Applications is an introductory text targeted to second or advanced first year undergraduate students. The organization of this text is motivated by what our experience tells us are the essential concepts that students should master in a one semester undergraduate Linear Algebra course. The centerpiece of our philosophy regarding the presentation of the material is that each topic should be fully developed before moving on to the next. In addition, there should be a natural connection between topics. We take great care to meet both of these objectives. This allows us to stay on task so that each topic can be covered with the depth required before progressing to the next logical one. As a result the reader is prepared for each new unit and there is no need to repeat a concept in a subsequent chapter when it is utilized.
Linear Algebra is taken early in an undergraduate curriculum and yet offers the opportunity to introduce the importance of abstraction, not only in mathematics, but in many other areas where Linear Algebra is used. Our approach is to take advantage of this opportunity by presenting abstract vector spaces as early as possible. Throughout the text, we are mindful of the difficulties that students at this level have with abstraction and introduce new concepts first through examples which gently illustrate the idea. To motivate the defini- tion of an abstract vector space, and the subtle concept of linear independence, we use addition and scalar multiplication of vectors in Euclidean Space. We have strived to create a balance between computation, problem solving, and ab- straction. This approach equips students with the necessary skills and problem solving strategies in an abstract setting that allows for a greater understanding and appreciation for the numerous applications of the subject.
