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