Ordinary Differential Equations

/Definition, reduction of explicit equations to first order/ /Existence and uniqueness of solutions/ /Differential inequalities/ Solutions to specific equations /One-dimensional time-independent equations of first or second order/ OLD TOC __NOTOC__ Ordinary Differential Equations covering uses of and solutions to ordinary differential equations thumb|right|400px|The Rössler Attractor. This chaotic system is generated by a system of ordinary differential equations. This book aims to lead the reader through the topic of differential equations, a vital area of modern mathematics and science. This book provides information about the whole area of differential equations, concentrating first on the simpler equations. Calculus Table of contents /Introduction/ /Preliminaries from calculus/ Form and Solutions of Differential Equations First-Order Differential Equations Separation of Variables Linear Differential Equations Exact Differential Equations Substitution Methods Bernoulli Equations Ricatti Equations Orthogonal and Oblique Trajectories Equations of higher degrees Equations without x or y Equations that are homogeneous in x and y d'Alembert's Equation Clairaut Equations Legendre Transformations Graphing Differential Equations Second-Order Differential Equations Constant Coefficients Series Solutions Hypergeometric Equation Frobenius Solution to the Hypergeometric Equation Legendre Equation Bessel Equation Mathieu Equation Continued Fraction Solutions Applications of Second-Order Differential Equations Higher Order Differential Equations Linear equations General Linear Equations Infinite Series Solutions to Linear Equations Integration methods Laplace Transform Bessel Function Euler Transform Mellin Transform Hypergeometric Series Double Integration /Sturm-Liouville theory/ Systems of linear differential equations /Nonlinear Systems/ /Green's Functions/ Existence and Uniqueness of Solutions /The Picard–Lindelöf theorem/ /Peano's theorem/ /Blow-ups and moving to boundary/ /Global uniqueness of solution over interval/ /Maximum domain of solution/ The Successive Approximations Method of Proof Applications to Linear Equations The Cauchy-Lipschitz Method of Proof Existence Theorems for Complex Numbers Continuous Transformation Groups Infinitesimal Transformations Invariant Functions /Glossary/ /List of Some Equations/ Help Needed /Roadmap/ Sources Differential Equations and Boundary Value Problems- C.H. Edwards Jr and David E. Penny MIT Open Courseware- http://ocw.mit.edu/index.html A Short Course in Ordinary Differential Equations Kong Qingkai 2014 Springer International Publishing Ordinary Differential Equations Walter Wolfgang 1998 Springer New York Mathematical analysis University level mathematics books O 25% Mathematical analysis University level mathematics books O 25%