• Announcements: Hello! The new homework set HW7 (which is the last one) is now available, and due on Dec 2. Recall that, because of the holiday, the next day of lecture and office hours is only next Monday. I hope everyone has a wonderful and safe Thanksgiving weekend!

• Video 1: Interchanging the order of limits under uniform convergence
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• Video 2: Uniform limit of continuous functions is continuous (and a partial converse)
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• Video 3: The vector space $\mathcal C(X,\mathbb R)$ of continuous and bounded real-valued functions
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• Video 4: Completeness of $\mathcal C(X,\mathbb R)$
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• Video 5: Uniform convergence and integration
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• Video 6: Uniform convergence and differentiation
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• Video 7 (Bonus material): A function that is everywhere continuous but nowhere differentiable
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• Some plots of partial sums $F_N(x)=\sum_{n=1}^N \left(\frac{3}{4}\right)^n\varphi(4^n x)$, such that $f(x)=\lim_{N\to+\infty} F_N(x)$ is the everywhere continuous but nowhere differentiable function from Video 7 are below, click to open image separately:

$1\leq N\leq 6$, for $x\in[-1,1]$

$1\leq N\leq 7$, for $x\in [0,2^{-N}]$

$8\leq N\leq 13$, for $x\in [0,2^{-N}]$