Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering.
Fundamentals of Differential Equations is designed for a one-semester sophomore or junior-level course.
Topics: Introduction, First-Order Differential Equations, Mathematical Models and Numerical Methods Involving First Order Equations, Linear Second-Order Equations, Introduction to Systems and Phase Plane Analysis, Theory of Higher-Order Linear Differential Equations, Laplace Transforms, Series Solutions of Differential Equations, Matrix Methods for Linear Systems, Partial Differential Equations, Eigenvalue Problems and Sturm-Liouville Equations, Stability of Autonomous Systems, Existence and Uniqueness Theory.