Theory of Ordinary Differential EquationsThis book has developed from courses given by the authors and probably contains more material than will ordinarily be covered in a one-year course. It is hoped that the book will be a useful text in the application of differential equations as well as for the pure mathematician. Prerequisite for this book is a knowledge of matrices and the essentials of functions in a complex variable. The book thoroughly addresses linear equations, and touches on the use of the Riemann-Stieltjes integral, and the Lebesgue integral, and the theorems required from integration theory. The problems, in some cases, give additional material not considered in the text. |
Contents
EXISTENCE AND UNIQUENESS OF SOLUTIONS | 1 |
EXISTENCE AND UNIQUENESS OF SOLUTIONS continued | 42 |
LINEAR DIFFERENTIAL EQUATIONS | 62 |
Copyright | |
27 other sections not shown
Other editions - View all
Theory of Ordinary Differential Equations Earl A. Coddington,Norman Levinson No preview available - 1955 |
Common terms and phrases
a₁ adjoint analytic assumed asymptotic B₁ boundary condition bounded variation c₁ c₂ Chap characteristic roots class Cą Clearly coefficients column completes the proof components Consider constant matrix continuous function convergent critical points denoted diagonal differential equation domain eigenfunctions eigenvalues equicontinuous exists finite number fixed formal series formal solution formula fundamental matrix given Green's formula Green's function hence HINT implies inequality integral interval L(C+ Lemma Let f limit-point linear system linearly independent linearly independent solutions monotone nonsingular matrix P₁ Parseval equality periodic orbit periodic solution plane polynomial Prob Proof of Theorem proves regular singular point result satisfies self-adjoint sequence Show solution of 1.1 solutions of Lx successive approximations Suppose t₁ tends Theorem 2.1 tion U₁ unique solution valid vanish vector