Linear Ordinary Differential Equations

Preface. 1. Simple Applications. Introduction; Compartment systems; Springs and masses; Electric circuits; Notes; Exercises; 2. Properties of Linear Systems. Introduction; Basic linear algebra; First-order systems; Higher-order equations; Notes; Exercises; 3. Constant Coefficients. Introduction; Properties of the exponential of a matrix; Nonhomogeneous systems; Structure of the solution space; The Jordan canonical form of a matrix; The behavior of solutions for large t; Higher-order equations; Exercises; 4. Periodic Coefficients. Introduction; Floquet's theorem; The logarithm of an invertible matrix; Multipliers; The behavior of solutions for large t; First-order nonhomogeneous systems; Second-order homogeneous equations; Second-order nonhomogeneous equations; Notes; Exercises; 5. Analytic Coefficients. Introduction; Convergence; Analytic functions; First-order linear analytic systems; Equations of order n; The Legendre equation and its solutions; Notes; Exercises; 6. Singular Points. Introduction; Systems of equations with singular points; Single equations with singular points; Infinity as a singular point; Notes; Exercises; 7. Existence and Uniqueness. Introduction; Convergence of successive approximations; Continuity of solutions; More general linear equations; Estimates for second-order equations; Notes; Exercises; 8. Eigenvalue Problems. Introduction; Inner products; Boundary conditions and operators; Eigenvalues; Nonhomogeneous boundary value problems; Notes; Exercises; 9. Eigenfunction Expansions. Introduction; Selfadjoint integral operators; Eigenvalues for Green's operator; Convergence of eigenfunction expansions; Extensions of the expansion results; Notes; Exercises; 10. Control of Linear Systems. Introduction; Convex sets; Control of general linear systems; Constant coefficient equations; Time-optimal control; Notes; Exercises; Bibliography.