ABSTRACT

Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete proble

chapter 1|10 pages

Introduction

chapter 2|94 pages

Linear Differential Equations

chapter 3|54 pages

Lie Transformation Groups

chapter 5|54 pages

Symmetries of Differential Equations

chapter 6|64 pages

Transformation to Canonical Form

chapter 7|40 pages

Solution Algorithms

chapter 8|4 pages

Concluding Remarks