The course explores the meaning of computing e^{pi i} and delves into the intricacies of the relationship between exponential functions. Students will learn about the properties of exp(x), visualization techniques, and the periodic nature of the relationship. The teaching method involves a live math session with questions, results, and visual aids. This course is intended for individuals interested in advanced mathematical concepts and those curious about the technical details behind Euler's formula.
Overview
Syllabus
Welcome.
Ending Animation Preview.
Reminders from previous lecture.
Q1: Prompt (Relationship with e^iθ=…).
Q1: Results.
WTF, Whats The Function.
Exploring exp(x).
Exploring exp(x) in Python.
Important exp(x) property.
Q2: Prompt (Given f(a+b) = f(a)f(b)…).
Ask: Which is more interesting, special cases or the general case.
Q2: Results.
Will a zero break Q2?.
The e^x convention.
Q3: Prompt (i^2 = -1, i^n = -1).
Ask: Zero does not break Q2.
Q3: Results.
Comparison to Rotation.
Visualizing this relationship.
The special case of π.
Periodic nature of this relationship.
Q4: Prompt (e^3i).
Q4: Results.
Explaining the celebrity equation.
Homework / Things to think about.
Ask: Zero does break Q2..
Closing Remarks.
Taught by
3Blue1Brown
