Ordinary Differential Equations

Ordinary differential equations are equations involving derivatives in one direction, to be solved for a solution curve.

Table of contents

• Introduction

Simple solution techniques

• Separable equations: Separation of variables
• One-dimensional first-order linear equations
• Two-dimensional exact differential equations
• Derived cases 1: Rational functions in the right hand side
• Derived cases 2: Bernoulli equations, Ricatti equations
• Derived cases 3: Euler factors

Theory of general explicit ODEs

• Preliminaries from calculus
• The Picard–Lindelöf theorem
• Peano's theorem
• Blow-ups and moving to boundary
• Dependence on parameters

Linear ODEs (higher order and multidimensional)

• Multidimensional linear equations with constant coefficients
• Linear autonomous equations of higher order with constant coefficients
• Homogenous linear equations with varying coefficients
• General linear equations
• Linear autonomous equations of higher order with varying coefficients

Sources

Differential Equations and Boundary Value Problems- C.H. Edwards Jr and David E. Penny
MIT Open Courseware- http://ocw.mit.edu/index.html

• Kong, Qingkai (0000). A Short Course in Ordinary Differential Equations. Universe: Publisher. 
• Walter, Wolfgang (1998). Ordinary Differential Equations. New York: Springer.