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The e^x convention
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Classroom Contents
What Is Euler's Formula Actually Saying? - Lockdown Live Math
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- 1 Welcome
- 2 Ending Animation Preview
- 3 Reminders from previous lecture
- 4 Q1: Prompt (Relationship with e^iθ=…)
- 5 Q1: Results
- 6 WTF, Whats The Function
- 7 Exploring exp(x)
- 8 Exploring exp(x) in Python
- 9 Important exp(x) property
- 10 Q2: Prompt (Given f(a+b) = f(a)f(b)…)
- 11 Ask: Which is more interesting, special cases or the general case
- 12 Q2: Results
- 13 Will a zero break Q2?
- 14 The e^x convention
- 15 Q3: Prompt (i^2 = -1, i^n = -1)
- 16 Ask: Zero does not break Q2
- 17 Q3: Results
- 18 Comparison to Rotation
- 19 Visualizing this relationship
- 20 The special case of π
- 21 Periodic nature of this relationship
- 22 Q4: Prompt (e^3i)
- 23 Q4: Results
- 24 Explaining the celebrity equation
- 25 Homework / Things to think about
- 26 Ask: Zero does break Q2.
- 27 Closing Remarks
