Theory of Ordinary Differential Equations
McGraw-Hill, 1955 - Differential equations - 429 pages
This 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.
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Existence and Uniqueness op Solutions continued
Linear Differential Equations
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actual analytic applied approximations associated assumed asymptotic bounded called Chap characteristic roots circle Clearly closed coefficients column complex components considered constant containing continuous function convergent corresponding curve defined definition denoted derivatives determined diagonal differential equation domain eigenfunctions eigenvalues elements equality equation equicontinuous example exists expansion fact finite fixed follows formal formula function fundamental matrix given gives hence holds implies inequality integral interval L(C+ Lemma limit linear system linearly independent matrix Moreover nonsingular obtains orbit origin periodic plane positive Prob problem proof Proof of Theorem proves relation REMARK replaced respect result satisfies self-adjoint sequence Show shown similar solutions of Lx space successive sufficiently Suppose tends Theorem 2.1 tion uniformly unique valid vanish vector yields zero