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Function Syntax Reference

Complete guide to mathematical function syntax supported by the Laplace Transform Calculator.

Syntax Rules

Always use * for multiplication
2*t (not 2t)
Use parentheses for clarity
sin(3*t) (not sin 3t)
Use exp() for exponentials
exp(-2*t) (not e^(-2*t))
Spaces are optional but recommended
2 * t or 2*t
Case sensitive function names
sin(t) (not SIN(t))

Basic Functions

t^n
Power functions
Syntax:
t^2, t^3, t^(-1)
Example:
t^2 → 2/s³
Constants
Numerical constants
Syntax:
1, 2, pi, e
Example:
1 → 1/s
Multiplication
Use * for multiplication
Syntax:
2*t, 3*sin(t)
Example:
2*t → 2/s²

Trigonometric Functions

sin(at)
Sine function
Syntax:
sin(3*t)
Example:
sin(3*t) → 3/(s²+9)
cos(at)
Cosine function
Syntax:
cos(3*t)
Example:
cos(3*t) → s/(s²+9)
tan(at)
Tangent function
Syntax:
tan(t)
Example:
tan(t) → Complex form

Exponential Functions

exp(at)
Exponential function
Syntax:
exp(-2*t)
Example:
exp(-2*t) → 1/(s+2)
e^(at)
Alternative syntax
Syntax:
exp(-2*t)
Example:
Use exp() instead of e^

Special Functions

heaviside(t-a)
Unit step function
Syntax:
heaviside(t-2)
Example:
heaviside(t-2) → exp(-2*s)/s
dirac(t-a)
Dirac delta function
Syntax:
dirac(t)
Example:
dirac(t) → 1
sqrt(t)
Square root function
Syntax:
sqrt(t)
Example:
sqrt(t) → sqrt(π)/(2*s^(3/2))

Hyperbolic Functions

sinh(at)
Hyperbolic sine
Syntax:
sinh(2*t)
Example:
sinh(2*t) → 2/(s²-4)
cosh(at)
Hyperbolic cosine
Syntax:
cosh(2*t)
Example:
cosh(2*t) → s/(s²-4)

Ready to try these functions?

Use our calculator to test any of these syntax examples