Ordinary Differential Equations

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 Problems Part 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 Domain Appendix A. Historical Note on Formal Methods of Integration Appendix B. Numerical Integration of Ordinary Differential Equations Appendix C. List of Journals Quoted in Footnotes to the Text Appendix D. Bibliography Index of Authors; General index