Lecture 21: The Riemann Integral of a Continuous Function

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Lecture 20: Taylor's Theorem and the Definition of Riemann Sums

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Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem

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Lecture 18: Weierstrass's Example of a Continuous and Nowhere Differentiable Function

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Lecture 17: Uniform Continuity and the Definition of the Derivative

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Lecture 16: The Min/Max Theorem and Bolzano's Intermediate Value Theorem

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Lecture 15: The Continuity of Sine and Cosine and the Many Discontinuities of Dirichlet's Function

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Lecture 14: Limits of Functions in Terms of Sequences and Continuity

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Lecture 13: Limits of Functions

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Lecture 12: The Ratio, Root, and Alternating Series Tests

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