This course explores compound interest, the mathematical constant e, and their relationship to circles. The learning outcomes include understanding the concept of imaginary interest rates, graphing relationships, and exploring mathematical connections. The course teaches skills such as graphing, analyzing interest equations, and compounding continuously with imaginary numbers. The teaching method involves live questions, prompts, results discussions, and visual animations. The intended audience for this course is individuals interested in advanced mathematical concepts and their applications.
Overview
Syllabus
Welcome.
Q1: Prompt (Would you take an imaginary interest rate).
"e to the pi i for dummies" video shoutout.
Q1: Results.
Q2: Prompt (two banks, two rates).
Ask: Beauty of connections in math.
Q2: Results.
Desmos for Q2.
Q3: Prompt (savings growth rate, 6% every 6mo).
Q3: Results.
Desmos graph explored.
Breaking down an interest rate.
An interesting interest equation.
Q4: Prompt (100*(1+0.12/n)^2 as n → ∞).
Ask: Quaternions.
Q4: Results.
Explaining Q4.
Defining e.
The definition of e from previous lectures.
The imaginary interest rate.
Graphing this relationship.
The imaginary interest rate animation.
Compounding continuously with i.
The spring & Hooke's law.
Q5: Prompt (Δx & Δv for a spring).
Ask: Rotation in for multiple dimensions.
Q5: Results.
Rewriting the spring's position.
Bringing it all together.
Ask: Hints on last lecture's homework.
Closing Remarks.
Taught by
3Blue1Brown
