Dror Bar-Natan: Classes: 2003-04: Math 157 - Analysis I:

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Homework Assignment 17

Assigned Tuesday January 27; due Friday February 6, 2PM, at SS 1071

This document in PDF: HW.pdf

Required reading. All of Spivak Chapter 18.

To be handed in. From Spivak Chapter 18: 1 (ii, v, ix), 4 (odd parts), 7 (odd parts), 8 (odd parts), 21, 47 (e).

Recommended for extra practice. From Spivak Chapter 18: 1 (the rest), 4 (even parts), 6, 7 (even parts), 8 (even parts), 18, 34, 47 (a-d), 49.

Aside. Here's a short Mathematica session that computes an approximation of the number $e$ for which $\int_1^e\frac{dt}{t}$:

drorbn@coxeter:~/classes/157AnalysisI:1 math
Mathematica 4.1 for IBM AIX
Copyright 1988-2000 Wolfram Research, Inc.

In[1]:= s = 0; t = 1; dt = 0.000001;

In[2]:= While[(s += dt/t) < 1, t += dt]; t

Out[2]= 2.71828

Just for fun. How far can you reach by stacking up $n$ identical domino pieces, before your tower will lean over and fall?

$$%% \input Dominos.epic$$

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