1. 1 Section 2 SECTION 2 Partial Fractions

2. 2 We need to split the following into separate terms: Roots of the denominator D(s): Case I – unrepeated factor Case II – repeated factor Case III – complex factors Case IV – repeated complex factors Section 2

3. 3 Case I – unrepeated factor example Section 2

4. 4 Use the "cover up" rule …

5. 5 Section 2 Inverse Laplace Transform:

6. 6 Section 2 example Inverse Laplace Transform:

7. 7 Section 2 Why does the "cover up" rule work ? alternative method solve these

8. 8 Question: Section 2 Obtain the Partial Fractions to

9. 9 Section 2 Case II – repeated factor example unrepeated factor repeated factor

10. 10 Section 2 Use the repeated factor rule …

11. 11 Section 2 Inverse Laplace Transform:

12. 12 Section 2 Case III – complex factors example complex conjugates Inverse Laplace Transform:

13. 13 Section 2 example Inverse Laplace Transform: where

14. 14 Section 2 (1)Attacking Polynomials Directly (rather than using the complex formulae) Other Topics not Covered Inverse Laplace Transform: using

15. 15 Section 2 (2) To solve these, you just use the methods of cases II and III, only with complex number calculations Case IV – repeated complex factors