In Differential Equations and Linear Algebra, Third Edition, the material on differential equations and linear algebra required in many sophomore courses for mathematics, science, and engineering majors is introduced. In S\Titing this text we have endeavored to develop an appreciation for the power of the general vector space framework in formulating and solsing linear problems. We have made every effort to lay forth the subject as we ourselves would naturally teach it, using an abundance of examples and illustrations throughout the exposition, but not at the expense of a deliberate, rigorous treatment. Our aim has been to present the material so that it is accessible to the student who has successfully completed three semesters of calculus, and it is definitely the intention that the student read the text, not just the examples. Almost all results are proved in detail. However, it is certainly possible to by-pass many of the proofs and use the text in a more problem solving based setting. Such an approach to the course could potentially incorporate some form of technology (computer algebra system (CAS) or graphing calculator) and there are many instances in the text where the power of technology is illustrated using the CAS Maple. Furthermore, a large majority of the exercise sets have problems that require some form of technology for their solution. These problems are designated with a o. As with the previous editions of this text, in developing the third edition we have kept maximum flexibility of the material in mind. In so doing, the text can effectively accommodate the different emphases that can be placed in a combined differential equa- tions and linear algebra course, the varying backgrounds of students who enroll in this type of course, and the fact that different institutions have different credit values for such a course. The whole text can be covered in a five credit-hour course.
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