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muijonathan.com | ||
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quomodocumque.wordpress.com
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| | | | | During the summer I gave a talk at PROMYS and afterwards had dinner with a bunch of the undergraduate teaching assistants. At one point I said, "The wonderful thing about math is that while of course we're proud of what we do, we also know that everything we make and understand would be made and... | |
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robertlovespi.net
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| | | | | I go by RobertLovesPi on-line, and am interested in many things. Welcome to my own little slice of the Internet, which is shared freely with anyone who is interested. The viewpoints and opinions expressed on this website are my own, except for the relatively small number of clearly-identified works of others. Nothing here should be... | |
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www.superprof.com
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| | | | | Explore our articles on algebra. The branch of mathematics dealing with symbols, equations, and the rules for solving problems and understanding relationships. | |
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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. | ||
