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math.andrej.com | ||
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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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gowers.wordpress.com
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| | | | | It's been a while since I have written a post in the "somewhat philosophical" category, which is where I put questions like "How can one statement be stronger than an another, equivalent, statement?" This post is about a question that I've intended for a long time to sort out in my mind but have found... | |
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mathenchant.wordpress.com
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| | | | | There are mathematical operations of all kinds with the property that doing the operation twice is tantamount to not doing anything at all. Such operations are called involutions, and you can find them all over the place in math: taking the negative of a number, taking the reciprocal of a number, rotating an object by... | |
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www.oneman-onemap.com
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