Ordinary differential equations (ODEs) and linear algebra are foundational post-calculus mathematics courses in the sciences. The goal of this text is to help students master both subject areas in a one-semester course. Linear algebra is developed first, with an eye toward solving linear systems of ODEs. A computer algebra system is used for intermediate calculations (Gaussian elimination, complicated integrals, etc.); however, the text is not tailored toward a particular system.
The book

• systematically develops the linear algebra needed to solve systems of ODEs;
• includes over 15 distinct applications of the theory, many of which are not typically seen in a textbook at this level (e.g., lead poisoning, SIR models, digital filters);
• emphasizes mathematical modelling; and
• contains group projects at the end of each chapter that allow students to more fully explore the interaction between the modelling of a system, the solution of the model, and the resulting physical description.

It is intended for students who have had one year of calculus and are taking a first class in ODEs.

Todd Kapitula is professor mathematics at Calvin College, Michigan. Prior to Calvin College, h taught at the University of New Mexico, Virginia Tech, and the University of Utah. He is the (co)author of over 45 peer-reviewed research articles, one of which won the SIAM Outstanding Paper Prize, and has been awarded several National Science Foundation research grants. He coauthored with Keith Promislow the graduate level text Spectral and Dynamical Stability of Nonlinear Waves (Springer, 2013). He is a member of SIAM and participates in the SIAM activity groups (SIAGs) on Applied Mathematics Education, Dynamical Systems, and Nonlinear Waves and Coherent Structures.

Preface; 1 Classification of Differential Equations; 2 Models in One Dimension; 3 Essential Linear Algebra; 4 Essential Ordinary Differential Equations; 5 Boundary Value Problems in Statics; 6 Heat Flow and Diffusion; 7 Waves; 8 First-Order PDEs and the Method of Characteristics; 9 Green’s Functions; 10 Sturm–Liouville Eigenvalue Problems; 11 Problems in Multiple Spatial Dimensions; 12 More about Fourier Series; 13 More about Finite Element Methods; Appendix A Proof of Theorem 3.47; Appendix B Shifting the Data in Two Dimensions; Bibliography; Index