MA1102 Calculus                                                                                                                                                          

General Advice

Whatever the reason that you choose to take up mathematics, upon admission and sifting through the official literature, there is the apprehension and anxiety about sustaining the interest in and coping with the subject. How do I learn the university mathematics? Is there any habit that I should cultivate or acquire towards a meaningful appreciation of the subject ? How can I effectively understand a mathematics lecture ? How much work and preparation do I need? Is group study helpful? These and many similar kind of questions, we hope we can help you find the answer. For different persons the answers may well be different.

Many of you come from different background. Some have 'A' levels or equivalent qualifications, others the international baccalaureate qualifications. It is important that you examine yourself either by going through some of the equivalent pre-university texts to bring your competence to a level that your lecturers expect. During the course of a complicated argument or explanation, a lecturer may well assume that you can handle the following topics easily and transparently. A lack in this ability may constitute a serious impediment to getting the most out of the course and may make the course less enjoyable.  For the success of the years at NUS, it is most important that you know these topics thoroughly and are able to work with them fluently, confidently and rapidly, enabling you to search and reach the deeper and sometimes unexpected results. Some of these results may or may not be examination materials, nevertheless a deeper understanding would be acquired through independently reached or derived paths. Along the way, your lecturer may show you a road map. Take time to explore and develop a feel of the length and breadth of the subject of mathematics. Return again and again to the road map, make your own personalised road map, make addition to it as you progress through the years. Chart your progress this way, no matter how small. Look deeper into yourself for that urge to search for truth, for that beauty hidden in mathematics.

The basic essential topics are:

(1) Arithmetic and algebraic manipulation

(2) Inequalities

(3) Trigonometric functions

(4) Differentiation

(5) Integration

The level of competency for topics (4) and (5) is expected only in manipulative skills. The skills and understanding will have to be better and deeper as you progress.

Lectures

Most mathematics modules are taught by a combination of lectures, tutorials and some such as MA1101 and MA1102 include computer laboratory sessions. If you are new to the university, all three modes of teaching may seem like strange experience.

The lecturer may or may not assign a text book but most will give you a few references and supplementary materials. Some will put the supplementary materials on a course web site and may give you other useful links and help there too, like the present guide. By and large, the lecturer will cover a part of the course in each lecture, presenting the theory and methods and probably doing some worked examples. The presentation may vary from chalk-board talk to a large screen presentation. Whatever the means, the lecturer would be giving you his carefully selected understanding to you, revealing the depths whenever he thinks the time is ripe for it, sketch the difficulty of the development of the topics historically and conceptually, show you the mathematical landscape and its beauty, point the way, and unreservedly giving all he knows. Be prepared to listen, open your mind to receive - the lecturer is an expert and it would be silly to ignore what is said. It is your responsibility to keep a record of what happens in the lecture, including whatever points that has also suddenly become clearer to you, a slide or video shown, computation done, etc. Get used to concentrate. This is easily said than done especially for those who find 50 minutes or an hour of concentration a strain. There is a number of ways to help yourself. Sit near the front, so you can hear better, see better and the strain will be lessened. Get used to taking good and accurate notes of what is said. Be sure to get most things down-- that does not mean copying every word the lecturer utters but the most important points, enabling the connection and details to be worked out and completed later. For this it is useful to write clearly and concisely, gather your thoughts accurately but don't let the recording interfere with your concentration. It is also useful to leave wide margin, you will need to annotate or add later or fill in some comment or understanding or points to follow up or even an alternate view point. Do ask questions during lectures. If there is something not clear to you, most likely it is also not clear to a lot of you.

Always regularly file your work i.e, annotated lecture notes and tutorial assignment with index and references to textbook, solved problems, examples, etc and also your reworked lecture notes. In this way, you will be helped to be prepared for the next lecture. Reserved especially a time slot for going through your notes and files before going to the next lecture. You should at least try to go through the ideas, concepts, examples, line by line, idea by idea of your last lecture. Having updated and filed notes will be a great help. But if you fall behind, it would take a lot of effort to catch up again.

Tutorials

For every module, you will have a tutor that will remain with you until the end of the course. The relationship between student and tutor is an important one. The tutor is there to help you, especially after an absence through illness, etc. Tutorial class size varies. A good part of the responsibility for making the tutorial useful and interesting lies with you. Below are some tips for making the most out of your tutorials.

  1. Always complete your tutorial assignment. For those questions you got stuck, examine yourself to see if you know why you got stuck. Jot down the reason. Have the questions ready for asking. It is also a good practice to make a note in the margin whenever there is a step you are not sure of. If you can work in a group, go through your difficulty with the members of the group, most likely they will have the same difficulty and collectively, you may be able to either overcome the difficulty or come to a better understanding of the difficulty.
  2. Tell your tutor (appropriately and politely, remember your relation with the tutor is an important one) precisely what you would like him or her to do.
  3. Bring your lecture notes to the tutorial. Mark in the parts you do not follow. Ask your tutor regarding your difficulty. For this have your questions ready.
  4. Make sure your tutor writes down enough for you to reconstruct the solution later.
  5. Ask some intelligent questions (but prepare them before hand), if there is time to spare.
  6. Most of all, express yourself. If you do not understand what the tutor has done, say so. The tutor will be most willing to help you understand and overcome your deficiencies.
     

     

Computer Laboratory Sessions

Many of you have used a computer, for word processing or making up a spreadsheet. It is not very different when you come to a Computer Lab sessions for MA1102 or MA1101. What is different is the software you use and what you are expected to get out of it. For MA1102 Calculus, the aim is to help understand the development of the concepts in calculus, enhance your conceptual understanding, visualise the applications and let you experiment and explore mathematical concepts in more than one way. Graphical visualisation is very important. On a conceptual level its limitation is also important. The exciting part is that you can see definitions and application at work. You can test out your ideas and see them taking forms or shapes either statically or dynamically. The learning does not end with the session; at anytime, if the lab is free you can request to use the lab to experiment or help you visualise what has been bothering you or to clear up some doubts. It is important that you learn the basics for the software well. For MA1102 it is Derive for Windows. You will only take a short time to learn the basics. Remember the mathematics is important here and not the programming; make sure you grasp the basics well and concentrate on the mathematics at hand. Here is some useful tips:

  1. Make sure you get to grip with the Derive For Windows basics so that you can use the software easily, fluently and rapidly. Ask your Lab assistant or Lab tutor for help if you need it.
  2. Always bring your lecture notes or text book to the lab sessions. When you have forgotten a definition, they will come in handy.
  3. Be prepared to think beyond what you can see on the screen. There are functions that do not display well their hidden properties. You may have to zoom in many times, possibly hundreds of times and this is where your conceptual understanding will be put to the test. If I cannot observe it graphically, how can I prove it?
  4. Remember lab sessions are not calculator sessions. At the end of each lab sessions, you must ask yourself: What have I got out of it? Did I get a better understanding? Did I learn something that I did not know before? You will learn to be careful about making what seems obvious conclusions. Very often they are wrong. For example, you will learn how to answer the question: if f ' (a) > 0, is the function f necessarily increasing around the point a ?
  5. Don't rush through the lab sessions. Make each session an enjoyable and memorable experience. It can be memorable: you might have experience like suddenly realising the importance of the phrase 'given any e > 0' in the definition of a limit. Remember you can complete your lab worksheet and hand in to your lab assistant after the designated lab session.

     

Guide and comment for tutorial assignment

Click the following for details

Tutorial 1

Tutorial 2

Tutorial 3

Tutorial 4

Tutorial 5

Tutorial 6

Tutorial 7

Tutorial 8

Tutorial 9

Tutorial 10

Tutorial 11

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