Ordinary Differential Equations and Applied Linear Algebra [Kapitula]

[mklabgr]

Ordinary Differential Equations and Applied Linear Algebra, Second Edition, by Todd Kapitula, is a 2026 SIAM textbook designed for a one-semester undergraduate course combining linear algebra and ordinary differential equations (ODEs). It begins with the essential tools of linear algebra—matrices, eigenvalues, eigenvectors, and related concepts—and then continually uses them to develop methods for solving ODEs. The book covers scalar first-order equations, systems of first-order linear equations, higher-order linear equations, discontinuous forcing and the Laplace transform, and an introduction to planar nonlinear systems.

A major emphasis of the second edition is connecting mathematical techniques with real-world modeling. Case studies include SIR epidemic models, lead poisoning, and strongly damped forced oscillators, while projects explore Google's PageRank algorithm, pollution in the Great Lakes, lead poisoning, and glucose–insulin interactions. The book also includes more than 300 online homework problems through myOpenMath. 

Overall, it presents linear algebra not as an isolated subject but as a practical framework for understanding dynamical systems and mathematical models, making the text particularly suitable for students in science, engineering, and applied mathematics. 

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