Sum and Difference of Formulas

Relationships of Hyperbolic and Trigonometric

P - Euler's Theorem

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Laplace Transform:

*s = θ + jw*w = 2πf (angular frequency)

Time Domain h(t) Complex Frequency Domain H(s)

1

t

tn

cos wt

sin wt

cosh wt

sinh wt

Theorems on Laplace Transform1. Linearity Property:*Constants can be taken out before transforming to Laplace.

2. First Shifting Theorem:

3. Second Shifting Theorem:

4. General Heaviside Step Function:

F - List of Formulas

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Initial Value Theorem and Final Value Theorem

*magkabaliktad

Laplace Transforms of Derivative:

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)

)

= 1.587

P - Assignment Part 1

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P - Assignment Part 2

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Laplace Transform:

*s = θ + jw*w = 2πf (angular frequency)

Time Domain h(t) Complex Frequency Domain H(s)

1

t

tn

\pppñqzsxqwpxsqa

cos wt

sin wt

cosh wt

sinh wt

Theorems on Laplace Transform1. Linearity Property:*Constants can be taken out before transforming to Laplace.

2. First Shifting Theorem:

3. Second Shifting Theorem:

M - Laplace and Inverse Laplace Transform

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4. General Heaviside Step Function:

Inverse Laplace Transform

H(s) h(t)

1

t

cos wt

sin wt

cosh wt

sinh wt

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M - Problems

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5.

Derivation #3

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Definition of Z-Transform:

The z-transform is the discrete-time counterpart of the Laplace transform.

the z-transform is defined as follows:

Z-Transform

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