Taylor polynomial expansions in one and several independent variables.
OTHER License
A Julia package for Taylor polynomial expansions in one or more independent variables.
Comments, suggestions and improvements are welcome and appreciated.
Taylor series in one variable
julia> using TaylorSeries
julia> t = Taylor1(Float64, 5)
1.0 t + 𝒪(t⁶)
julia> exp(t)
1.0 + 1.0 t + 0.5 t² + 0.16666666666666666 t³ + 0.041666666666666664 t⁴ + 0.008333333333333333 t⁵ + 𝒪(t⁶)
julia> log(1 + t)
1.0 t - 0.5 t² + 0.3333333333333333 t³ - 0.25 t⁴ + 0.2 t⁵ + 𝒪(t⁶)
Multivariate Taylor series
julia> x, y = set_variables("x y", order=2);
julia> exp(x + y)
1.0 + 1.0 x + 1.0 y + 0.5 x² + 1.0 x y + 0.5 y² + 𝒪(‖x‖³)
Differential and integral calculus on Taylor series:
julia> x, y = set_variables("x y", order=4);
julia> p = x^3 + 2x^2 * y - 7x + 2
2.0 - 7.0 x + 1.0 x³ + 2.0 x² y + 𝒪(‖x‖⁵)
julia> ∇(p)
2-element Array{TaylorN{Float64},1}:
- 7.0 + 3.0 x² + 4.0 x y + 𝒪(‖x‖⁵)
2.0 x² + 𝒪(‖x‖⁵)
julia> integrate(p, 1)
2.0 x - 3.5 x² + 0.25 x⁴ + 0.6666666666666666 x³ y + 𝒪(‖x‖⁵)
julia> integrate(p, 2)
2.0 y - 7.0 x y + 1.0 x³ y + 1.0 x² y² + 𝒪(‖x‖⁵)
For more details, please see the docs.
TaylorSeries
is licensed under the MIT "Expat" license.
TaylorSeries
can be installed simply with using Pkg; Pkg.add("TaylorSeries")
.
There are many ways to contribute to this package:
This project began (using python
) during a Masters' course in the postgraduate
programs in Physics and in Mathematics at UNAM, during the second half of 2013.
We thank the participants of the course for putting up with the half-baked
material and contributing energy and ideas.
We acknowledge financial support from DGAPA-UNAM PAPIME grants PE-105911 and PE-107114, and DGAPA-PAPIIT grants IG-101113, IG-100616, IG-100819 and IG-101122. LB acknowledges support through a Cátedra Moshinsky (2013).