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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