Linear algebra and ordinary differential equations (ODEs) are foundational postcalculus mathematics. The goal of this text is to help students master both subject areas in a one-semester course. The linear algebra necessary for applications is developed first and continually referenced when solving ODEs. The discussion of ODEs focuses on solving linear problems since they are most relevant to undergraduate science courses that require an ODE background. Separable equations and nonlinear systems are also covered. New to the second edition are: case studies at the end of every chapter, addressing SIR models, a model for lead poisoning, and the dynamics for strongly damped forced oscillators among others, projects at the end of each chapter that enable students to explore the interaction between the creation of a mathematical model, the solution of the model, and the physical implications of the mathematical solution. including those on the Google PageRank algorithm, the flow of pollution in the Great Lakes, lead poisoning, and glucose/insulin interactions in the bloodstream, and access to over 300 online homework problems embedded within the CMS myOpenMath. Audience This book is meant for a one-semester course for which a treatment of linear algebra and ODEs is needed. The book assumes no linear algebra background. Students who have a background will find the survey of key linear algebra concepts in the first chapter a helpful refresher.