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Homework Assignment 9

Assigned Tuesday November 4; due Friday November 14, 2PM, at SS 1071

This document in PDF: HW.pdf

Required reading. All of Spivak Chapter 9.

To be handed in. From Spivak Chapter 9: Problems 1, 9, 15, 23.

Recommended for extra practice. From Spivak Chapter 9: Problems 8, 11, 21, 28.

Just for fun. Write a computer program that will allow you to draw the graph of the function

$\displaystyle f(x)=\sum_{n=0}^\infty \frac{1}{2^n}\sin 3^nx, $

and will allow you to zoom on that graph through various small ``windows''. Use your program to convince yourself that $ f$ is everywhere continuous but nowhere differentiable. The best plots will be posted on this web site! (Send pictures along with window coordinates by email to drorbn@math.toronto.edu).

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Dror Bar-Natan 2003-11-04