Math 409-502Harold P. [email protected] examination is Monday, November 1.The exam will have a similar format to the format of the first exam.The exam covers material through section 13.4.Daylight Saving Time ends this weekend:set your clock back one hour.Math 409-502 October 29, 2004 — slide #2Properties of continuous functionsA continuous function on a compact interval• is bounded;• attains a maximum value and attains a minimum value;• has the intermediate-value property.Put together, these properties say that the range is a compact interval.Preview of coming attractionAfter the exam, we will see in section 13.5 that another item can be added to the list: a continu-ous function on a compact interval is uniformly continuous.Math 409-502 October 29, 2004 — slide #3Examples related to exercise 13.1/1A union of compact intervals can be a non-compact interval.Example 1:∞Sn= 1[1n, 1] = (0, 1]Example 2:∞Sn= 1[0, n] = [0, ∞)Math 409-502 October 29, 2004 — slide #4Power series are continuous functionsIf the series∞∑n= 1anxnhas radius of convergence R, then this series is a continuous function onthe open interval (−R, R).Math 409-502 October 29, 2004 — slide #5HomeworkStudy for the examination.Math 409-502 October 29, 2004 — slide
View Full Document
Unlocking...