**Problems**

*You need to do exercises – all of the following you should be able to attempt. Do as many as you can/ want in the following order of most beneficial:*

*Wills’ Exercise Sheets
*

Q. 11-13 from http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise3.pdf

Q. 1 from http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise4.pdf

*Past Exam Papers*

Q. 4(b) from http://booleweb.ucc.ie/ExamPapers/exams2008/Maths_Stds/MS2001Sum08.pdf

Q. 4 from http://booleweb.ucc.ie/ExamPapers/Exams2008/MathsStds/MS2001a08.pdf

Q. 4(a) from http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/MS2001Sum06.pdf

Q. 5(a) from http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/Autumn/ms2001Aut.pdf

Q 5(a) from http://booleweb.ucc.ie/ExamPapers/exams2004/Maths_Stds/MS2001aut.pdf

Q. 5(a) from http://booleweb.ucc.ie/ExamPapers/exams2003/Maths_Studies/MS2001.pdf

Q. 5(a) from http://booleweb.ucc.ie/ExamPapers/exams2003/Maths_Studies/ms2001aut.pdf

Q. 5(a) from http://booleweb.ucc.ie/ExamPapers/exams2001/Maths_studies/MS2001Summer01.pdf

Q. 5 from http://booleweb.ucc.ie/ExamPapers/exams/Mathematical_Studies/MS2001.pdf

*From the Class*

1. *Prove Proposition 4.2.1 for the case that the minimum, differs from .*

*2. Drawings can be deceptive! Draw a function that is continuous on a closed interval but not differentiable at any point in the interval. What does your drawing suggest? Now see http://en.wikipedia.org/wiki/Weierstrass_function*

*3. Prove Proposition 4.2.3 (iii)*

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