Syntax

Description

Examples

Handle Expressions Involving Dirac and Heaviside Functions

Compute derivatives and integrals of expressions involving the Dirac delta and Heaviside functions.

Find the first and second derivatives of the Heaviside function. The result is the Dirac delta function and its first derivative.

syms x
diff(heaviside(x), x)
diff(heaviside(x), x, x)

ans =
dirac(x)
 
ans =
dirac(1, x)

Find the indefinite integral of the Dirac delta function. The integral of the Dirac delta function is the Heaviside function.

int(dirac(x), x)

ans =
heaviside(x)

Find the integral of this expression involving the Dirac delta function.

syms a
int(dirac(x - a)*sin(x), x, -Inf, Inf)

ans =
sin(a)

Use Assumptions on Variables

dirac takes into account assumptions on variables.

syms x real
assumeAlso(x ~= 0)
dirac(x)

ans =
0

For further computations, clear the assumptions.

syms x clear

Evaluate the Dirac delta Function for Symbolic Matrix

Compute the Dirac delta function of x and its first three derivatives.

Use a vector n = [0, 1, 2, 3] to specify the order of derivatives. The dirac function expands the scalar into a vector of the same size as n and computes the result.

n = [0, 1, 2, 3];
d = dirac(n, x)

d =
[ dirac(x), dirac(1, x), dirac(2, x), dirac(3, x)]

Substitute x with 0.

subs(d, x, 0)

ans =
[ Inf, -Inf, Inf, -Inf]

Input Arguments

See Also

heaviside | kroneckerDelta