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Group IS or Group ARE? | Collective Nouns: When to Use IS and When to Use ARE | English with Ananya
🤔 "The team IS playing well." — Correct 🤔 "The team ARE playing well." — Also Correct 🤔 So... which one is actually right? And how do you choose? This is one of the most debated and most confusing grammar questions in the English language — and even advanced learners get it wrong, or worse, avoid using these sentences altogether ...
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Runge Kutta Examples
Runge's phenomenon: when equally spaced nodes betray you. Increase the degree of your interpolating polynomial, and instead of converging, it explodes near the endpoints of [-1,1]. The culprit isn't the function's real-line behaviour — it's complex singularities hiding just off the axis, silently poisoning the convergence that equally spaced nodes can never achieve. Thankfully chebyshev interpolation points save the day!
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Runge's phenomenon: when equally spaced nodes betray you. Increase the degree of your interpolating polynomial, and instead of converging, it explodes near the endpoints of [-1,1]. The culprit isn't the function's real-line behaviour — it's complex singularities hiding just off the axis, silently poisoning the convergence that equally spaced nodes can never achieve. Thankfully chebyshev interpolation points save the day!
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