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Exploring π, i, and Series: A Quick Introduction to Their Values and Importance

Join David Monroe and Daniel Newton as they delve into the concepts of π, i, and series, addressing questions on values, convergence, derivatives, and trigonometry. Discover the relationship between e^(i*π)+1=0 and explore Taylor series.

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Exploring π, i, and Series: A Quick Introduction to Their Values and Importance

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Presentation Transcript

  1. “i” Love π Flavored Series By David Monroe and Daniel Newton

  2. BEFORE WE BEGIN • Don’t worry, we will not go crazy in depth • Feel free to do research on your own afterwards • Save “bigger picture” questions until our quick break

  3. Introduction: π,i, and • What are they? • What are their values? • Does the square root of a negative number have use? • Why mention them together? • Why does e^(i*π)+1=0?

  4. Series • What are series, and why are they important? • Are infinite series infinite, and what does it mean to converge?

  5. Derivatives • So what is a derivative? • How do they relate to series?

  6. Trigonometry • Another thing to learn? • Why do we care about them? • Does this relate to derivatives or series?

  7. Questions and Cookie Pizza π What questions do you have so far? Let us discuss them over a slice of π!

  8. Back to Series • Piecing it all together • Relating this to e, π, andi • https://www.desmos.com/calculator/gokjepwgi6

  9. Taylor Series • What make a series a Taylor series? • How does this relate sin and cosine to this?

  10. Common Taylor Series

  11. The Derivation (The Main Event!)

  12. Discussion • So what? • What else? • Final thoughts?

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