4 Calculus of Differential Algebra

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李群分析在地球物理流体动力学中的应用作者：Ranis Ibragimov,Nail Ibragimov　　 ISBN：978-7-04-031954-5　出版时间：2011-04-25

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目录

Front Matter

Part I InternalWaves in Stratified Fluid

1 Introduction

2 Governing Equations

3 Two Model Examples

Part II Introduction to Lie Group Analysis

4 Calculus of Differential Algebra

5 Transformation Groups

6 Symmetry of Differential Equations

7 Applications of Symmetry

Part III Group Analysis of InternalWaves

8 Generalities

9 Conservation Laws

10 Group Invariant Solutions

A Resonant Triad Model

References

Index
- 4.1 Definitions
- 4.1.1 Main variables
- 4.1.2 Total differentiations
- 4.1.3 Differential functions
- 4.1.4 Euler-Lagrange operator
- 4.2 Properties
- 4.2.1 Divergence test
- 4.2.2 One-dimensional case
- 4.3 Exact equations
- 4.3.1 Definition
- 4.3.2 First-order equations
- 4.3.3 Second-order equations
- 4.3.4 Linear second-order equations
- 4.4 Change of variables in the space A
- 4.4.1 One independent variable
- 4.4.2 Several independent variables

4 Calculus of Differential Algebra

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