Lie Theory of One-Parameter Groups - Abraham B. Cohen
Lie Theory of One-Parameter Groups with Diff. Eqs. - Table of Contents
1. Lie’s Theory of One-Parameter Groups
2. Differential Equations of the First Order
3. Miscellaneous Theorems and Geometrical Applications
4. Differential Equations of the Second and Higher Orders
5. Linear Partial Differential Equations of the First Order
6. Ordinary Differential Equations of the Second Order
7. Contact Transformations
What You Will Learn in Lie Theory of One-Parameter Groups with Diff. Eqs.
"An Introduction to the Lie Theory of One-Parameter Groups; with Applications to the Solution of Differential Equations" by "Abraham B. Cohen" is a focused and accessible introduction to "Lie theory", written for students and readers who want to understand how symmetry methods can be used to solve differential equations. The book explains the basic ideas of continuous transformation groups in a clear, step-by-step manner, making an advanced topic easier to approach.
A major strength of the text is its direct connection between theory and application. Cohen shows how "one-parameter groups" can be applied to "ordinary differential equations" to reduce their order or simplify them into solvable forms. By working through examples, the reader learns how invariance and symmetry provide powerful tools beyond standard solution techniques. This practical emphasis helps bridge classical differential equation methods and more modern analytical approaches.
The book is especially valuable for advanced undergraduates, graduate students, and researchers interested in "applied mathematics" and mathematical physics. Its clear exposition and systematic development make it a useful reference for anyone studying symmetry methods in differential equations. Even today, the book remains relevant for understanding the foundations of Lie group applications in solving differential equations.
Book Details & Specifications
Title:
Lie Theory of One-Parameter Groups - Abraham B. Cohen
Publisher:
D. C. Heath & Co.,
Year:
1911
Pages:
272
Type:
PDF
Language:
English
ISBN-10 #:
1429700602
ISBN-13 #:
978-1429700603
License:
Public Domain Work
Amazon:
Amazon
About the Author: Abraham B. Cohen
The author
Abraham B. Cohen
was a mathematician and educator known for his work in "Lie theory" and "differential equations", with a strong focus on teaching advanced ideas clearly. He specialized in explaining how "one-parameter groups" and "symmetry methods" can be used to analyze mathematical problems, especially in applied mathematics. In his work, Cohen connected abstract theory with practical techniques for solving equations, making his writing useful for students and researchers. His book highlights the role of "Lie groups", "differential equations", and "mathematical analysis" in understanding structure and symmetry, and it remains a valuable reference for those studying theoretical and applied mathematics.
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