Category: mathematics |
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mathscholar.org
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[AI summary] The text presents a detailed, self-contained proof of the Fundamental Theorem of Calculus (FTC) using basic principles of calculus and real analysis. It breaks the proof into two parts: Part 1 establishes that the integral of a continuous function defines a differentiable function whose derivative is the original function, and Part 2 shows that the definite integral of a continuous function can be computed as the difference of an antiderivative evaluated at the endpoints. The proof relies on lemmas about continuity, differentiability, and the properties of integrals, avoiding advanced techniques. The text is structured to provide a clear, step-by-step derivation of the FTC for readers familiar with calculus fundamentals.
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blog.plover.com
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From the highly eclectic blog of Mark Dominus
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ionathan.ch
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[AI summary] This post explores the concept that many interesting problems in various fields occur at small values of n, discussing examples from logic, computics, mathematics, and physics.
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