Ordinary Differential Equations: with Lie's Theory by J. M. Page
Ordinary Differential Equations: with Lie's Theory - Table of Contents
1. Genesis of the Ordinary Differential Equation in Two Variables
2. The Simultaneous System and the Equivalent Linear Partial Differential Equation
3. Finite and Infinitesimal Transformations in the Plane
4. Exact and Invariant Differential Equations of the First Order
5. Geometrical Applications of the Integrating Factor: Orthogonal Trajectories and Isothermal Systems
6. Differential Equations of the First Order but Not of the First Degree: Singular Solutions
7. Riccati’s Equation and Clairaut’s Equation
8. Total Differential Equations of the First Order and Degree in Three Variables Derivable from a Single Primitive
9. Ordinary Differential Equations of the Second Order in Two Variables
10. Ordinary Differential Equations of the mth Order in Two Variables
11. The General Linear Differential Equation in Two Variables
What You Will Learn in Ordinary Differential Equations: with Lie's Theory
"Ordinary Differential Equations: An Elementary Text-Book, with an Introduction to Lie’s Theory of the Group of One Parameter" by "James Morris Page" is a well-structured introductory book aimed at students learning the fundamentals of ordinary differential equations. It explains standard solution methods for first- and higher-order equations in a clear and systematic way, making it suitable for undergraduate mathematics, physics, and engineering students. The presentation emphasizes understanding techniques through carefully explained examples rather than heavy abstraction.
A notable strength of the book is its inclusion of "Lie’s theory of one-parameter groups" at an elementary level. Page shows how symmetry methods can be used to reduce and solve "ordinary differential equations", helping readers see connections between classical solution techniques and more advanced mathematical ideas. This approach provides historical and theoretical context while remaining accessible to beginners.
Because of its balanced treatment of theory and application, the book serves both as a primary learning text and as a bridge to more advanced studies in "differential equations" and "applied mathematics". Even today, it remains valuable for readers interested in classical methods, symmetry analysis, and the early development of Lie theory in differential equations.
Book Details & Specifications
Title:
Ordinary Differential Equations: with Lie's Theory by J. M. Page
Publisher:
Macmillan
Year:
1897
Pages:
251
Type:
PDF
Language:
English
ISBN-10 #:
1112414711
ISBN-13 #:
978-1112414718
License:
Public Domain Work
Amazon:
Amazon
About the Author: J. M. Page (James Morris Page)
The author
J. M. Page (James Morris Page)
was a mathematician and educator known for his clear teaching of ordinary differential equations. His books were written for students, focusing on logical explanations and practical methods that made difficult topics easier to understand. Page emphasized clarity and step-by-step reasoning in mathematical learning. He is especially recognized for introducing Lie’s theory of one-parameter groups at an elementary level. By connecting symmetry methods with differential equations, he helped bridge classical analysis and applied mathematics, leaving a lasting impact on mathematical education.
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