Скачать или смотреть Approximation of Functions Using Orthogonal polynomials | Legendre & Chebyshev Polynomials

Want to learn how to *approximate functions using orthogonal polynomials* like *Legendre* and **Chebyshev**? This step-by-step tutorial breaks it all down — perfect for math, physics, and engineering students!

🔥 *In This Video, You'll Learn:*
✅ What orthogonal polynomials are and why they matter
✅ How to derive Legendre and Chebyshev polynomials
✅ How to use them to approximate functions like \( f(x) = e^x \)
✅ Step-by-step method to compute approximation coefficients \( a_n \)
✅ Integration techniques, recurrence formulas & solved examples

📊 *Example Problem:*
We use *Legendre series* to approximate \( e^x \) over the interval \([-1, 1]\). You’ll see the full derivation, from the weight function to final expression.

⏱️ *Timestamps for Easy Navigation:*
00:00 - Introduction
01:30 - What are Orthogonal Polynomials?
04:45 - Legendre Polynomials Explained
10:15 - Deriving Coefficients for Approximation
17:00 - Example: Approximate \( e^x \)
23:45 - Using Chebyshev Polynomials


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✅ Improved Tags (With More Long-Tail Keywords)

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