I am emailing a link of this to everyone on the class list every Friday afternoon. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.ie and I will add you to the mailing list.

## Homework

Please find the Homework. Before you open it don’t be too alarmed: you only have to do ONE of the NINE options. All of the options are about differential calculus:

1. Nowhere-Continuous Functions
2. Intermediate Value Theorem
3. Fixing Nasty Functions and Making them Nice
4. Summarise Limits & Continuity
5. “Leaving Cert Questions”
6. L’Hopital’s Rule
7. Linear Algebra
8. Summarise Differentiation
9. Extrema of Functions of Several Variables with an Application to Statistics — contains a typo. Q.9 (a) should read “Show that (1, 1) and (−1,- 1) are local minima…” not “Show that (1, 1) and (−1, 1) are local minima…”. Also you can find the partial derivatives $\frac{\partial S}{\partial m}$ and $\frac{\partial S}{\partial c}$ without multiplying out $S(m,c)$

I am not going to pretend that this is an easy assignment, but I will say that clear and logical thinking will reveal that the solutions and answers aren’t ridiculously difficult: a keen understanding of the principles of differential calculus should see you through.

Roughly, I have gone with less thinking & more writing or more thinking & less writing but half the battle here is picking an option that you think you can do well.

The final date for submission is 01 February 2013 and you can hand up early if you want. You will be submitting to the big box at the School of Mathematical Science. If I were you I would aim to get it done and dusted early.

Note that you are will be free to collaborate with each other and use references but this must be indicated on your hand-up in a declaration. Evidence of copying or plagiarism will result in divided marks or no marks respectively. You will not receive diminished marks for declared collaboration or referencing although I demand originality of presentation. If you have a problem interpreting any question feel free to approach me, comment on the webpage or email.

Ensure to put your name, student number, module code (MS 2001), and your declaration on your homework.

## Lectures

We have finished up to but not including Section 3.2

## Tutorials

Remember you can ask whatever you want in tutorials. If you have questions about the test or past exam papers work away.

### Tutorial 7 Question Bank

Questions 3, 5, 7, 8, 13, 16, 17 from Exercise Sheet 3.

Question 3 from MS2001: Problems (after page 102 in the notes)

Questions 14, 20, 29, 35  from the Additional but Harder Exercises for Definitions II (two after page 108 in the notes).

### Tutorial 6 Question Bank

Questions 1, 2, 3 (i), (iii), 4, 7 (i), 8 (a) (i), (ii), 9, 13 (i) from Exercise Sheet 3.

Questions 35  from the Additional but Harder Exercises for Definitions II (two after page 108 in the notes).

### Tutorial 5 Question Bank

Questions 6 (iv), (v), (vii), 8, 9  from Exercise Sheet 2 — but don’t worry about removable and essential discontinuities (after page 62 in the notes).

Question 1 from MS2001: Problems (after page 108 in the notes)

Questions 1, 2, 3, 10, 11, 12, 13, 27  from the Additional but Harder Exercises for Definitions II (two after page 108 in the notes).

### Tutorial 4 Question Bank

Question 10 from Exercise Sheet 1 (after page 59 in the notes)

Questions 5, 6 (i), (ii), (iii), 7  from Exercise Sheet 2 — but don’t worry about removable and essential discontinuities (we are using the terms skip-discontinuity and blow-up) (after page 62 in the notes)

Question 1 from MS2001: Exercises (before page 63 in the notes)

Questions 23, 31- 37 from the Additional but Harder Exercises for Definitions I (just before page 60 in the notes).

### Tutorial 3 Question Bank

Question 9 from Exercise Sheet 1 (after page 59 in the notes)

Questions 1 – 4 from Exercise Sheet 2 (after page 62 in the notes)

Questions 4 from MS2001: Exercises (before page 63 in the notes)

Questions 27 – 30 from the Additional but Harder Exercises for Definitions I (just before page 60 in the notes).

### Tutorial 2 Question Bank

Questions 4, and 6 – 8 from Exercise Sheet 1 (after page 59 in the notes).

Questions 1 – 3 from MS2001: Exercises (before page 63 in the notes)

Questions 17 – 22 and 24 – 26 from the Additional but Harder Exercises for Definitions I (just before page 60 in the notes).

### Tutorial 1 Question Bank

Questions 1, 2 and 5 from Exercise Sheet 1 (after page 59 in the notes).

Questions 1 to 16 from the Additional but Harder Exercises for Definitions I (just before page 60 in the notes).