Linear Ordinary Differential Equations

Abstract

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.