Power Geometry in Algebraic and Differential Equations pdf epub mobi txt 电子书 下载 2025
- 数学
- in
- and
- Power
- Geometry
- Equations
- Differential
- Algebraic
- 几何学
- 代数方程
- 微分方程
- 数学
- 高等数学
- 几何方法
- 代数方法
- 微分几何
- 方程求解
- 数学物理
具体描述
The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed. The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems. The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics. The calculus also gives classical results obtained earlier intuitively and is an alternative to Algebraic Geometry, Differential Algebra, Lie group Analysis and Nonstandard Analysis.
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