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Compounding continuously with i
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Classroom Contents
Imaginary Interest Rates - Lockdown Live Math
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- 1 Welcome
- 2 Q1: Prompt (Would you take an imaginary interest rate)
- 3 "e to the pi i for dummies" video shoutout
- 4 Q1: Results
- 5 Q2: Prompt (two banks, two rates)
- 6 Ask: Beauty of connections in math
- 7 Q2: Results
- 8 Desmos for Q2
- 9 Q3: Prompt (savings growth rate, 6% every 6mo)
- 10 Q3: Results
- 11 Desmos graph explored
- 12 Breaking down an interest rate
- 13 An interesting interest equation
- 14 Q4: Prompt (100*(1+0.12/n)^2 as n → ∞)
- 15 Ask: Quaternions
- 16 Q4: Results
- 17 Explaining Q4
- 18 Defining e
- 19 The definition of e from previous lectures
- 20 The imaginary interest rate
- 21 Graphing this relationship
- 22 The imaginary interest rate animation
- 23 Compounding continuously with i
- 24 The spring & Hooke's law
- 25 Q5: Prompt (Δx & Δv for a spring)
- 26 Ask: Rotation in for multiple dimensions
- 27 Q5: Results
- 28 Rewriting the spring's position
- 29 Bringing it all together
- 30 Ask: Hints on last lecture's homework
- 31 Closing Remarks
