Linear Ordinary Differential Equations

Preface Chapter 1: Simple Applications. Introduction Compartment systems Springs and masses Electric circuits Notes Exercises Chapter 2: Properties of Linear Systems. Introduction Basic linear algebra First-order systems Higher-order equations Notes Exercises Chapter 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 Chapter 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 Chapter 5: Analytic Coefficients. Introduction Convergence Analytic functions First-order linear analytic systems Equations of order n The Legendre equation and its solutions Notes Exercises Chapter 6: Singular Points. Introduction Systems of equations with singular points Single equations with singular points Infinity as a singular point Notes Exercises Chapter 7: Existence and Uniqueness. Introduction Convergence of successive approximations Continuity of solutions More general linear equations Estimates for second-order equations Notes Exercises Chapter 8: Eigenvalue Problems. Introduction Inner products Boundary conditions and operators Eigenvalues Nonhomogeneous boundary value problems Notes Exercises Chapter 9: Eigenfunction Expansions. Introduction Selfadjoint integral operators Eigenvalues for Green's operator Convergence of eigenfunction expansions Extensions of the expansion results Notes Exercises Chapter 10: Control of Linear Systems. Introduction Convex sets Control of general linear systems Constant coefficient equations Time-optimal control Notes Exercises Bibliography.