Symmetry methods have long been recognized to be of great importance for the study of the differential equations arising in mathematics, physics, engineering, and many other disciplines. The purpose of this book is to provide a solid introduction to those applications of Lie groups to differential equations which have proved to be useful in practice, including determination of symmetry groups, integration of orginary differential equations, construction of group-invariant solutions to partial differential equations, symmetries and conservation laws, generalized symmetries, and symmetry methods in Hamiltonian systems. The computational methods are presented so that grauate students and researchers in other fields can readily learn to use them. Following an exposition of the applications, the book develops the underlying theory. Many of the topics are presented in a novel way, with an emphasis on explicit examples and computations. Further examples, as well as new theoretical developments, appear in the exercises at the end of each chapter. This second edition contains a new section on formal symmetries and the calculus of pseudo-differential operators, simpler proofs of some theorems, new exercises, and a substantially updated bibiography.
發表於2024-12-23
Applications of Lie Groups to Differential Equations (Graduate Texts in Mathematics) 2024 pdf epub mobi 電子書 下載
圖書標籤: 數學 PDE Lie-Group 李群
李群理論的本質在於非綫性的條件綫性化瞭
評分李群理論的本質在於非綫性的條件綫性化瞭
評分李群理論的本質在於非綫性的條件綫性化瞭
評分李群理論的本質在於非綫性的條件綫性化瞭
評分李群理論的本質在於非綫性的條件綫性化瞭
Applications of Lie Groups to Differential Equations (Graduate Texts in Mathematics) 2024 pdf epub mobi 電子書 下載