Mathematics Packages

DifferentialEquations.jl2841Multilanguage suite for highperformance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differentialalgebraic equations (DAEs), and more in Julia.

Symbolics.jl1353Symbolic programming for the next generation of numerical software

ForwardDiff.jl888Forward Mode Automatic Differentiation for Julia

DynamicalSystems.jl834Award winning software library for nonlinear dynamics and nonlinear timeseries analysis

StaticArrays.jl761Statically sized arrays for Julia

Gridap.jl691Gridbased approximation of partial differential equations in Julia

LightGraphs.jl671An optimized graphs package for the Julia programming language

Tullio.jl605⅀

ApproxFun.jl537Julia package for function approximation

SymbolicUtils.jl537Symbolic expressions, rewriting and simplification

OrdinaryDiffEq.jl533High performance ordinary differential equation (ODE) and differentialalgebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

Interpolations.jl523Fast, continuous interpolation of discrete datasets in Julia

Measurements.jl486Error propagation calculator and library for physical measurements. It supports real and complex numbers with uncertainty, arbitrary precision calculations, operations with arrays, and numerical integration.

Grassmann.jl464⟨GrassmannCliffordHodge⟩ multilinear differential geometric algebra

Graphs.jl457An optimized graphs package for the Julia programming language

TensorOperations.jl450Julia package for tensor contractions and related operations

ChainRules.jl435Forward and reverse mode automatic differentiation primitives for Julia Base + StdLibs

AlgebraOfGraphics.jl421Combine ingredients for a plot

IterativeSolvers.jl401Iterative algorithms for solving linear systems, eigensystems, and singular value problems

Meshes.jl389Computational geometry in Julia

DSP.jl379Filter design, periodograms, window functions, and other digital signal processing functionality

Manifolds.jl368Manifolds.jl provides a library of manifolds aiming for an easytouse and fast implementation.

SpecialFunctions.jl350Special mathematical functions in Julia

GeometricFlux.jl348Geometric Deep Learning for Flux

TaylorSeries.jl346Taylor polynomial expansions in one and several independent variables.

Roots.jl342Root finding functions for Julia

Ferrite.jl339Finite element toolbox for Julia

Oscar.jl339A comprehensive open source computer algebra system for computations in algebra, geometry, and number theory.

Krylov.jl338A Julia Basket of HandPicked Krylov Methods

DiffEqSensitivity.jl329A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimizethendiscretize, discretizethenoptimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

SciMLSensitivity.jl329A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimizethendiscretize, discretizethenoptimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

NLsolve.jl324Julia solvers for systems of nonlinear equations and mixed complementarity problems

StructArrays.jl319Efficient implementation of struct arrays in Julia

DiffEqBase.jl309The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems

LinearMaps.jl303A Julia package for defining and working with linear maps, also known as linear transformations or linear operators acting on vectors. The only requirement for a LinearMap is that it can act on a vector (by multiplication) efficiently.

LazyArrays.jl303Lazy arrays and linear algebra in Julia

Polynomials.jl303Polynomial manipulations in Julia

BifurcationKit.jl301A Julia package to perform Bifurcation Analysis

FastGauss.jl298Julia package for Gaussian quadrature

FastGaussQuadrature.jl298Julia package for Gaussian quadrature
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