Neil E. Cotter

Associate Professor (Lecturer)

Last Updated: 3/5/21

Laplace transform

Definition

Laplace Cards

Page 1 t-domain v1.2 (pdf)

Page 1 s-domain v1.2 (pdf)

Page 2 t-domain v1.2 (pdf)

Page 2 s-domain v1.2 (pdf)

Step functions

Piecewise function defs

Example (pdf)

Transform pairs

Table of basic transforms | (pdf)

Impulse function

Step function

Sine

Example (pdf)

Example 2 (pdf)

Identities:

List | (pdf)

Multiplication by constant

Addition

Differentiation

Integration

Delay

Frequency shift

Scaling time

Multiplication by time (pdf)

Example 1 (pdf)

Example 2 (pdf)

Example 3 (pdf)

Example 8 | (pdf)

Example 9 (pdf)

Inverse transform

†Definition

Partial fractions

Complex root identity (pdf)

Example 1 (pdf)

Example 2 (pdf)

Example 3 (pdf)

Example 4 (pdf)

Example 5 (pdf)

Example 6 (pdf)

Example 7 | (pdf)

Matching forms

Example 1 (pdf)

Complex roots

Example 1 (pdf)

Poles and zeros

Pole location vs t form | (pdf)

RC Filter

Example 1 | (pdf)

Example 2 (pdf)

Example 3 | (pdf)

Example 4 (pdf)

Initial/final value theorems

†Initial value theorem (pdf)

Example (pdf)

Example 2 | (pdf)

Example 3 (pdf)

Circuits

s-domain circuit elements

R L C | (pdf)

Initial Conditions | (pdf)

Example (pdf)

s-domain solutions

Example (pdf)

Example 2 (pdf)

Example 3 (pdf)

Example 4 (pdf)

t-domain waveforms

Example (pdf)

Example 2 (pdf)

Example 3 (pdf)

Example 4 (pdf)

Example 5 (pdf)

Example 6 (pdf)

Impulse function

Example (pdf)

Basis functions

Sinusoids as eigenfunctions

Transfer functions

Magnitude and phase

j encodes phase

Matrix differential equations

Transfer function stability

Final value theorem

State-space equations