Ordinary Differential Equations (eBook)

Edward L. Ince (Autor)

eBook Download: EPUB

2012
Dover Publications (Verlag)
978-0-486-15821-1 (ISBN)

Infos

Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; much more. "Highly recommended" — Electronics Industries.

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The theory of ordinary differential equations in real and complex domains is here clearly explained and analyzed. Not only classical theory, but also the main developments of modern times are covered. Exhaustive sections on the existence and nature of solutions, continuous transformation groups, the algebraic theory of linear differential systems, and the solution of differential equations by contour integration are as valuable to the pure mathematician as the fine treatment of the equations of Legendre, Bessel, and Mathieu, the conditions for the oscillatory character of solutions of a differential equation, and the relation between a linear differential system and an integral equation are to the engineer and the physicist.Partial contents: real domain (elementary methods of integration, the existence and nature of solutions, continuous transformation-groups, linear differential equations-the general theory, with constant coefficients, solutions, algebraic theory, Sturmian theory, and later developments); complex domain (existence theorems, equations of first order, non-linear equations of higher order, solutions, systems, classifications of linear equations, oscillation theorems)."e;Highly recommended."e; — Electronics Industries. "e;Deserves the highest praise."e; — Bulletin, American Mathematical Society.

Inhalt

Part I. Differential Equations in the Real Domain I. Introduction II. Elementary Methods of Integration III. The Existence and Nature of Solutions of Ordinary Differential Equations IV. Continuous Transformation-Groups V. The General Theory of Linear Differential Equations VI. Linear Equations with Constant Coefficients VII. The Solution of Linear Differential Equations in an Infinite Form VIII. The Solution of Linear Differential Equations by Definite Integrals IX. The Algebraic Theory of Linear Differential Systems X. The Sturmian Theory and its Later Developments XI. Further Developments in the Theory of Boundary ProblemsPart II. Differential Equations in the Complex Domain XII. Existence Theorems in the Complex Domain XIII. Equations of the First Order But Not of the First Degree XIV. Non-Linear Equations of Higher Order XV. Linear Equations in the Complex Domain XVI. The Solution of Linear Differential Equations in Series XVII. Equations with Irregular Singular Points XVIII. The Solution of Linear Differential Equations by Methods of Contour Integration XIX. Systems of Linear Equations of the First Order XX. Classification of Linear Differential Equations of the Second Order with Rational Coefficients XXI. Oscillation Theorems in the Complex DomainAppendix A. Historical Note on Formal Methods of IntegrationAppendix B. Numerical Integration of Ordinary Differential EquationsAppendix C. List of Journals Quoted in Footnotes to the TextAppendix D. Bibliography Index of Authors; General index

Produkt-Details

• Erscheint lt. Verlag: 27.4.2012
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Gewicht: 649 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• ISBN-10: 0-486-15821-7 / 0486158217
• ISBN-13: 978-0-486-15821-1 / 9780486158211