This tried-and-true book of differential equations expands upon the authors' Differential Equations: Computing and Modeling, 2nd Edition. It covers the core concepts and techniques of elementary linear algebra—matrices and linear systems, vector spaces, eigensystems, and matrix exponentials—that are needed for a careful introduction to linear equations. Complimenting this solid foundation, the book emphasizes mathematical modeling of real-world phenomena, and offers a fresh new computational flavor evident in figures, examples, problems, and projects throughout. Chapter topics include: first order differential equations, mathematical models and numerical methods, linear systems and matrices, vector spaces, linear equations of higher order, eigenvalues and eigenvectors, linear systems of differential equations, matrix exponential methods, and nonlinear systems and phenomena. A geometric visualization for those interested in science and engineering.