By Dongming Wang
This e-book provides the cutting-edge in tackling differential equations utilizing complicated tools and software program instruments of symbolic computation. It makes a speciality of the symbolic-computational elements of 3 varieties of primary difficulties in differential equations: remodeling the equations, fixing the equations, and learning the constitution and homes in their options. The 20 chapters are written via best specialists and are based into 3 parts.
The e-book is worthy interpreting for researchers and scholars engaged on this interdisciplinary topic yet can also function a important reference for everybody attracted to differential equations, symbolic computation, and their interaction.
Read Online or Download Differential Equations with Symbolic Computation PDF
Similar mathematics books
It is a finished creation to Landau Lifshitz equations and Landau Lifshitz Maxwell equations, starting with the paintings through Yulin Zhou and Boling Guo within the early Eighties and together with many of the paintings performed via this chinese language crew led through Zhou and Guo on the grounds that. The e-book makes a speciality of facets comparable to the lifestyles of susceptible options in multi dimensions, life and distinctiveness of soft ideas in a single size, kin with harmonic map warmth flows, partial regularity and very long time behaviors.
- Potential Theory (2nd Edition) (Universitext)
- Multidimensional Integral Equations and Inequalities
- Solutions Manual to Accompany Ordinary Differential Equations
- Advanced courses of mathematical analysis II: proceedings of the 2nd international school, Granada, Spain, 20-24 September 2004
- A Boundedness Criterion via Atoms for Linear Operators in Hardy Spaces
- Mathematical, philosophical, religious and spontaneous students' explanations of the paradox of Achilles and the tortoise
Additional info for Differential Equations with Symbolic Computation
Ideally, to obtain the common solutions for the intersections of the ﬁrst ﬁve quadratic terms, we would like to compute their Gr¨ o¨bner basis with respect to a lexicographic ordering. Unfortunately, the computations are suﬃciently diﬃcult that such an approach does not work directly. However, we can compute a Gr¨ o¨bner basis with a total degree ordering, which is much more eﬃcient computationally, but less useful for obtaining explicit equations for the zeros of the polynomials. If the ideal was zero dimensional, then we could use the FGLM algorithm to return eﬃciently to a lexicographic basis, but in our case, it turns out that there is a non-trivial one dimensional solution (also shared by the sixth quadratic term).
5. 4) are also isochronous center conditions. 5) holds. 5) and the recursive formulas in Appendix B, we have, after careful computations, τ5 = 2b21 , −(a03 b03 ) + 4 λ , τ10 = 2 −(a12 2 b03 ) − a03 b12 2 τ15 = , 8 −(a03 2 b03 2 ) τ20 = . 5), it is easy to get the following result. 6. 17) λ = a21 = b21 = a30 = b30 = a03 = b03 = 0. 3) are zero. 7, the origin is an isochronous center. 3) becomes dz 2 a12 w6 z 5 3 b12 w4 z 7 =z+ + , dT 5 5 dw 3 a12 w7 z 4 2 b12 w5 z 6 = −(w + + ). 19) becomes u (10 u − 11 a12 v + b12 u12 v 9 − 2 a12 b12 u11 v 10 + a12 2 b12 u10 v 11 ) du = = U, dT 10 (u − a12 v) dv v (−10 u + 9 a12 v + b12 u12 v 9 − 2 a12 b12 u11 v 10 + a12 2 b12 u10 v 11 ) = = −V.
We note that an immediate corollary of the work is that there are components of the center variety of the class of all cubic systems which have codimension 12. ˙ adek. The result for cubic systems was ﬁrst shown by Zol ¸ However, the system he considers is diﬀerent from ours. This is because, as noted in his paper, it is not possible to generate 11 limit cycles from his system by considering the linear terms only. The nice thing about the result here is that it depends on only the simplest arguments and a direct calculation.
Differential Equations with Symbolic Computation by Dongming Wang