**Lecturer:** Mr. J.P. McCarthy

**Office:** Mathematics Research, Western Gateway Building

Meetings by appointment via email only.

**Email:** jippo@campus.ie

**Web:** *https://jpmccarthymaths.wordpress.com*

This page will comprise the webpage for this module and as such shall be the venue for course announcements including definitive dates for the test and the homework. This page shall also house such resources as a copy of this initial handout, the exercises, a copy of Stephen Wills’ course notes, links (such as to Stephen Wills’ webpage for this module and to exam papers), as well supplementary material. Please note that not all items here are relevant to MS 2001; only those in the category `MS 2001′. Feel free to use the comment function therein as a point of contact.

**Module Objective:** To provide an introduction to techniques and applications of differential calculus.

**Module Content:** Limits, continuity and derivatives of functions of one variable. Applications.

**Assessment:** Total Marks 100: End of Year Written Examination 75 marks; Continuous Assessment 25 marks.

**Continuous Assessment:** 25 \% of your final mark will come from two equal weighted in-class tests. The first in-class test will probably take place on 27/10/10 and the second on 8/12/10. The webpage will contain

the latest and definitive information about these.

Absence from the test will not be considered unless accompanied

by a reasonable excuse (requiring medical cert or similar), in which case special arrangements will come into force.

The marks you obtain for the continuous assessment will be carried forward

to the Autumn exam.

**Lectures:** Monday 3-4, WGB G08; Wednesday 9-10 WGB G14. Please note that the lectures will be conducted in a very methodical way. This module aims to give a rigorous development of differential calculus and the material presented in class will be `bare-bones’ and largely free of explanation and remarks. It will be vital to attend lectures as explanations and remarks shall be given verbally and in passing (e.g. on a margin of the whiteboard). Even more importantly, in terms of your attendance, these `bare-bones’ notes will only be presented in class and shall not be made available electronically. Even in the unlikely case of these notes being made available, the worked examples won’t be contained in them and the solutions will only be presented in lectures.

For those foolish enough to miss lectures, Stephen Wills’ lecture notes *do *contain explanations. When looking for an explanation of a particular topic open the pdf file and please use CTRL-F to find the key term.

**Tutorials:** There will be a weekly tutorial starting in the third week of term (5/10/10): Tuesday 1-2 WGB G04. Please email me if this time clashes with another lecture, etc. There are many ways to learn maths. Two methods which aren’t going to work are

*reading your notes and hoping it will all sink in**learning off a few key examples, solutions, etc.*

By far and away the best way to learn maths is by *doing exercises*, and there are two main reasons for this. The best way to learn a mathematical fact/ theorem/ etc. is by using it in an exercise. Also the doing of maths is a skill as much as anything and requires practise. After the summer lay off you may find yourself rusty in terms of algebra. Regularly doing exercises will eliminate small slips and mistakes.

There is no shortage of exercises for you to try. The webpage contains a link to a set of exercises. Stephen Wills’ page contains several exercise sheets. Past exam papers are fair game. Also during lectures there will be some things that will be *left as an exercise.* How much time you can or should devote to doing exercises is a matter of personal taste, however tutorials will be far more productive for both you and I if you have at least attempted some exercises.

The format of tutorials is that those of you who have questions shall have them answered by me. No secrets will be divulged at tutorials and they are primarily for students who have questions about exercises. More general questions on course material shall be answered also. If there are no questions you shall be asked to do some exercises in class. Feel free at this point to put your hand up for some one-to-one attention.

THINK OF TUTORIALS AS FREE GRINDS!

**Reading:** Your primary study material shall be the material presented in the lectures. Exercises done in tutorials may comprise further worked examples. While the lectures will present everything you need to know about MS 2001, they will not detail *all *there is to know about calculus. Further references are to be found in the library: in or nearby section 515 – anything with the word ‘Calculus’ in the title shall be relevant. The webpage will contain supplementary material, and contains links and pieces about topics that are at or beyond the scope of the course. Stephen Wills’ notes provide a comprehensive reference also. Finally the internet provides yet another resource. Even Wikipedia isn’t too bad for this area of mathematics! You

are encouraged to exploit these resources; they will also be useful for MS2002 and MS3003.

**Exam:** The exam format will be the same as 2007-10. Acceding to the maxim that *learning off a few key examples, solutions, etc.* is bad and *doing exercises is good*, solutions to past papers shall not be made available. Only by trying to do the exam papers yourself can you guarantee proficiency. If you are still stuck at this stage feel free to ask the question come tutorial time.

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