Ordinary Differential Equations

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). "Highly recommended." — *Electronics Industries.* "Deserves the highest praise." — *Bulletin, American Mathematical Society.* * * * [Bordoni's Aug 2014 article on Boussinesq](https://isidore.co/calibre/browse/book/5141) mentions [singular solutions](https://www.encyclopediaofmath.org/index.php/Singular_solution) of differential equations, which Ince describes on pp. §§3.6, 3.51, 4.7, A.5. Ince is also cited in "[Lie Symmetry Methods for Solving Nonlinear ODEs](https://reference.wolfram.com/language/tutorial/DSolveLieSymmetryMethods.html);" re: Lie, cf. Ince pt. 1 ch. 4 ("Continuous Transformation-Groups"): "§4·1. Lie’s Theory of Differential Equations," which is a very good, insightful intro. to transformation groups applied to DEs. "§2·71. The Equivalent Partial Differential Equation" on characteristics Cover; Title Page; Copyright Page; Preface; Contents; Part I: Ifferential Equations in the Real Domain; I. Introductory; 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