Linear Algebra with Applications is an
introductory text targeted to second or advanced first year
undergraduates in engineering or mathematics. The organization of this
text is motivated by the authors' experience which tells them what
essential concepts should be mastered by students in a one semester
undergraduate Linear Algebra course. The authors' main objectives are
to fully develop each topic before moving on and to connect topics
naturally. The authors take great care to meet both these objectives,
because this organization will allow instructors teaching from this text
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. This
text is geared towards an introductory linear algebra course taken by
first or second year undergraduate students. However, it offers the
opportunity to introduce the importance of abstraction, not only in
mathematics, but in many other areas where Linear Algebra is used. The
textbook’s approach is to take advantage of this opportunity by
presenting abstract vector spaces as early as possible. Throughout the
text, the authors 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 definition of
an abstract vector space, and the subtle concept of linear
independence, the authors use addition and scalar multiplication of
vectors in Euclidean Space. The authors have strived to create a
balance between computation, problem solving, and abstraction. 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.