Integration and ODEs (scipy.integrate)

Integrating functions, given function object

quad(func, a, b[, args, full_output, ...])	Compute a definite integral.
dblquad(func, a, b, gfun, hfun[, args, ...])	Compute a double integral.
tplquad(func, a, b, gfun, hfun, qfun, rfun)	Compute a triple (definite) integral.
nquad(func, ranges[, args, opts, full_output])	Integration over multiple variables.
fixed_quad(func, a, b[, args, n])	Compute a definite integral using fixed-order Gaussian quadrature.
quadrature(func, a, b[, args, tol, rtol, ...])	Compute a definite integral using fixed-tolerance Gaussian quadrature.
romberg(function, a, b[, args, tol, rtol, ...])	Romberg integration of a callable function or method.
quad_explain([output])	Print extra information about integrate.quad() parameters and returns.
newton_cotes(rn[, equal])	Return weights and error coefficient for Newton-Cotes integration.
IntegrationWarning	Warning on issues during integration.

Integrating functions, given fixed samples

trapz(y[, x, dx, axis])	Integrate along the given axis using the composite trapezoidal rule.
cumtrapz(y[, x, dx, axis, initial])	Cumulatively integrate y(x) using the composite trapezoidal rule.
simps(y[, x, dx, axis, even])	Integrate y(x) using samples along the given axis and the composite Simpson’s rule.
romb(y[, dx, axis, show])	Romberg integration using samples of a function.

See also

scipy.special for orthogonal polynomials (special) for Gaussian quadrature roots and weights for other weighting factors and regions.

Integrators of ODE systems

odeint(func, y0, t[, args, Dfun, col_deriv, ...])	Integrate a system of ordinary differential equations.
ode(f[, jac])	A generic interface class to numeric integrators.
complex_ode(f[, jac])	A wrapper of ode for complex systems.
solve_bvp(fun, bc, x, y[, p, S, fun_jac, ...])	Solve a boundary-value problem for a system of ODEs.