1. Inverse Laplace Transforms (ILT)
3 basic cases
Distinct poles
Repeated poles
Complex conjugate poles

2. Basic facts/techniques that YOU will use
Partial Fraction Expansion (PFE)
ALGEBRA
You must use my approach.

3. Preliminary Example

4. Partial Fraction Expansion
Factor denominator into linear factors with coefficient of s being 1 in each factor.
Break up big fraction into sum of simple fractions (Partial fractions) with linear denominator.
Use formulas to ILT each term (terms are ADDED together, factors are multiplied)
Use algebra to simplify (get rid of j’s)

5. Example 1

6. “Cover up rule” Choose a denominator
Multiply both sides by denominator
Evaluate both sides at the s that makes the denominator 0.
Only numerator over chosen denominator survives.
Choose next denominator, etc.
You MUST USE COVER UP RULE

7. Example 2

8. Example 3

9. ILT, PFE, Cover up Rule distinct roots, multiple roots
Real roots, complex conjugate pairs of roots
Expect a 3rd or 4th order test problem
Calculator only used to find roots of denominators
Going from roots to factors
Show all work, No work  No credit