Here is the collection of some standard formulas in Laplace transform.

**Formulas in Laplace transform**

**Definition of Laplace transform**

Laplace transform of any function is defined as

**Standard formulas for Laplace transform of algebraic & exponential functions**

(a)

(b)

(c)

**Standard formulas for Laplace transform of trigonometric & hyperbolic functions**

(a)

(b)

(c)

(d)

**First shift theorem**

If then

**Multiplying by **

So, for

**Dividing by **

If then

**Inverse transform**

If then

**Laplace transform is a linear transform.**

This means

(a)

(b)

Here is a non-zero scalar quantity.

**Laplace transform of derivatives**

(a)

(b)

(c)

Here

and at .

**Heaviside unit step function**

Heaviside unit step function is: f(t) = u (t – c)

**Laplace transform of Heaviside unit step function **

(a)

(b) where .

**Second shift theorem**

If , then where is real and positive.

There’s still more to come. I’ll add them later.

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