For courses in Differential Equations and Linear Algebra in departments of math and engineering. This text covers the core concepts and techniques of elementary linear algebramatrices and linear systems, vector spaces, eigensystems, and matrix exponentialsthat are needed for a careful introduction to differential equations. The differential equations and linear algebra are well-integrated. Complementing this solid foundation, the text emphasizes mathematical modeling of real-world phenomena, and offers a fresh new computational flavor evident in figures, examples, problems, and projects throughout.