PART 1

THE LAPLACE TRANSFORMS

6.2. Defination of Laplace Transform

6.2. Defination of Laplace Transform

a)

b)

c)

Example 6.2.

Solution:

Hence;

6.3. Properties of Laplace Transform1. Linearity

6.3. Properties of Laplace Transform2. Scalling

3. Time Shift

6.3. Properties of Laplace Transform

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6.3. Properties of Laplace Transform

6.3. Properties of Laplace Transform4. Frequency Shift

6.3. Properties of Laplace Transform5. Time Differantiation

6.3. Proporties of Laplace Transform

6.3. Properties of Laplace Transform

6.3. Properties of Laplace Transform6. Time Integration

6.3. Properties of Laplace Transform

6. Frequency Differantiation

6.3. Properties of Laplace Transform

7. Time Periodicity

Taking Laplace transform of each term;

8. Initial and Final Values

For initial values;

For an example;

Then;

For Final Value;

For Example;

As another example;

This is incorrect !!!!