- Colloquia
- Dawood, “Mathematical Methods in Equity Research”
- Thursday, February 19, 3:00 - 4:00, Newton 203
- Dickerson, “Mathematics Majors’ Understandings of the
Concept of Mathematical Definition”
- Monday, February 23, 4:00 - 5:00, Newton 201
- Extra credit for summaries
- Dawood, “Mathematical Methods in Equity Research”
- Section 8.5
- Separating fractions into parts to integrate
- Factor denominator into f1 f2 …
- Write fraction as A/f1 + B/f2 + …
- Or (Ax+B)/f if f of form (ix2 + jx + k)
- Where do A, B, etc. come from?
- Heaviside method?
- Examples
- Integrate 1 / (x-1)(x+3)
- Key steps:
- Write equation equating integrand to sum of fractions with factors as denominators and unknown numerators A and B
- Cross-multiply to remove fractions from equation
- Group coefficients of x and constant term together
- Coefficients of x, constant have to be equal on both sides of equation, so you get a system of equations that defines A, B. Solve it.
- Use A and B values to rewrite original integral as sum of simpler integrals, and integrate them
- Key steps:
- Integrate 1 / (x-1)(x+3)
- More partial fractions
- Try doing Heaviside method on above example as a starting point