- 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”
- Problem set
- Examples
- Find coefficients for 1 / (x-1)(x+3) using Heaviside method
- Integrate (x+2) / (x2-1)
- First trick is to factor denominator into (x-1)(x+1)
- First trick is to factor denominator into (x-1)(x+1)
- Integrate (x2+3x) / (x-1)(x-5)2
- (x-5)2 gives rise to two terms in partial fraction decomposition: B/(x-5) and C/(x-5)2
- Solve for A, B, and C using Heaviside tactic for A and C,
and then finding value B would have to have to make equation
hold for x=0
- x=0 is a more or less arbitrary choice of x value that
is easy to calculate with and keeps all denominators defined
- x=0 is a more or less arbitrary choice of x value that
is easy to calculate with and keeps all denominators defined
- But doesn’t book have an example that suggests this
should use (Cx + D) / (x-5)2?
- Not quite. You need such a term in cases involving x2
that can’t be factored, but not when x2
(or higher powers) just arise from a repeated factor
- Not quite. You need such a term in cases involving x2
that can’t be factored, but not when x2
(or higher powers) just arise from a repeated factor
- Find coefficients for 1 / (x-1)(x+3) using Heaviside method
- Finish partial fractions