Power geometry in algebraic and differential equations /
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 d...
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Language Notes: | English. |
| Published: |
Amsterdam ; New York :
Elsevier,
2000.
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| Edition: | 1st ed. |
| Series: | North-Holland mathematical library ;
v. 57. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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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| Physical Description: | 1 online resource (ix, 385 pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 359-381) and index. |
| ISBN: | 9780444502971 0444502971 9780080539331 0080539335 1281038725 9781281038722 9786611038724 6611038728 |