Introduction to Ordinary Differential equations / Shepley L. Ross

Table of Content
1 Differential equations and their
solutions
1.1 Classification of differential equations; their origin and application
1.2 Solution
1.3 Initial-value problems, boundary-value problems and existence of solutions

2 First-order equations for which exact solutions are obtainable
2.1 Exact differential equations and integrating factors
2.2 Separable equations reducible to this form
2.3 Linear equations and Bernoulli equations
2.4 Special integrating factors and transformations

3 Applications of first-order equations
3.1 Orthogonal and oblique Trajectories
3.2 Problems in mechanics
3.3 Rate problems

4 Explicit methods of solving higher-order linear differential equations
4.1 Basic theory of linear differential equations
4.2 The homogeneous linear equation with constant coefficients
4.3 The method of undetermined coefficients
4.4 Variations of parameters
4.5 The cauchy-euler equation

5 Applications of second-order linear differential equations with constant Coefficients
5.1 The differential equations of the vibrations of a mass on spring
5.2 Free, undamped motion
5.3 Free damped motion
5.4 Forced motion
5.5 Resonance phenomena

6 Series solutions of linear differential equations
6.1 Power series solutions about an ordinary point
6.2 Solutions about singular points: the methods of Frobenius
6.3 Bassel's equations and bassel functions

7 System Linear differential equations
7.1 Differential operators and an operator method
7.2 Applications
7.3 Basic theory of linear systems in normal form: two equations in two unknown functions
7.4 Homogeneous linear systems with constant coefficients: two equations in two unknown functions
7.5 Matrices and vectors

8 Approximate methods of solving first order equations
8.1 Graphical methods
8.2 Power series methods
8.3 The method of successive approximations
8.4 Numerical methods

9 The Laplace transform
9.1 Definition, existence and basic properties of the Laplace transform
9.2 The inverse transform and the convolution
9.3 Laplace transform solution of linear differential equations with constant coefficients
9.4 Laplace transform solution of linear systems .

Includes Index: p 429-432