The Seventeenth Week: Elementary methods of solving Differential Equations

Michio Kuga

A chapter in Galois’ Dream: Group Theory and Differential Equations, 1993, pp 109-113 from Springer

Abstract: Abstract Let us consider a set Σ of “known functions”. We regard every constant as a known function. The following procedures are used often to produce new functions out of old (known) functions F1, F2,...: (i) The four operations of arithmetic: $$\begin{array}{*{20}{c}} {{{F}_{1}},{{F}_{2}} \to {{F}_{1}} + {{F}_{2}}} \\ {{{F}_{1}},{{F}_{2}} \to {{F}_{1}} - {{F}_{2}}} \\ {{{F}_{1}},{{F}_{2}} \to {{F}_{1}} \cdot {{F}_{2}}} \\ {{{F}_{1}},{{F}_{2}} \to {{F}_{1}}/{{F}_{2}}} \\ \end{array}$$ Linear combinations: $${F_1},{F_2} \to {\lambda _1}{F_1} + {\lambda _2}{F_2}$$ (ii) Differentiation: $$F \to \frac{{dF}}{{dz}}$$ (iii) Integration: $$F\left( z \right) \to \int {F\left( z \right)dz} $$ (iv) Exponentiation: $$F\left( z \right) \to {e^{F\left( z \right)}}$$

Date: 1993
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0329-2_18

Ordering information: This item can be ordered from
http://www.springer.com/9781461203292

DOI: 10.1007/978-1-4612-0329-2_18

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().