URL http://www.mast.queensu.ca/~helena/math006

Math 006 - Introduction to Calculus


Brief notes for each week
Hints for assignements
Hints Two
Hints Three
Solutions to sample quizzes
Handout for week 3 Handout for week 4 Handout for week 5 Handout for week 6 Handout for week 7 Handout for week 8 Handout for week 9 Handout for week 10
Handout for week 11
Handout for week 12
Marks


Please see Handout for week 12 for a list of exam type questions. I expect to have the Marks page updated and completed about 20 April - please check that your final marks add up!


Useful stuff to know

I'm Helena Verrill, teacher of Math 006 for Winter 1998.

My office is room 401, Jeffery Hall.

If you have any questions about the course come to see me in my office hours, or ask after class, or email me, or ring my office, 545 2417.

Details of exams, homework, office hours, etc

Office hours

Monday 2-3.30 Wednesday 2-3.30 Friday 2-3.30

Tutorial

Room 116, Tuesday 2.30 - 3.30

TA: Margret Spicer, office 222 (if you need help outside my office hours and can't find me, try Margret, who will post her office hours outside her door).

Exams

Midterm

The midterm exam will last 1 hour, and will take place the first Wednesday after the break. In that class we will have 30 minutes for a quick review and questions, then the test, and then you may leave. (Ie no new material will be lectured).

Final exam

Will probably be held at the normal lecture time. Date to be announced.

Marks

You will be able to find a chart showing your progress here. (This will appear as soon as the first assignment and first quiz has been marked).

The marking scheme for the course will be as follows:

Notices

Check the notice boards outside the lecture room (1st floor Jeffrey) for answers to quizzes, sample quizzes, and homework solutions (posted after everything's been handed in). I'll be able to pin written things up faster than I can type things in to these web pages.

list of material that is (or has been) on the notice boards. (After taking down previous weeks homework solutions they will go on reserve in a file with the other stuff in Douglas for your reference.)

You can take things down from the notice boards to photocopy on the first floor, but please put them back up again as soon as possible (ie, no more than 10 minutes later.)

Things on reserve

I will put photocopies of the lecture overheads into Douglas, on reserve, the day after the lecture, so you can reread them if you wish. The text book is also on reserve in Douglas library.

Handouts

Where to get handouts

So you make sure you have any handouts you should have got in lectures, I will make a list here, and also put copies of hand outs on reserve in Douglas library. I will also put up the list of assignments on the notice board outside the lecture room.

List of Handouts


IMPORTANT

Because of the cancelled class on the 14th, the lecture on Limits will be on the 21 of January instead. We will not rush to cram everything in to one week instead of two now, possibly we may have to miss out some details later on in the course, eg, slightly briefer on antiderivates and integrals. But since it looks like there will be three extra days added on to the length of term, we should be able to have an extra lecture at the end to make up for the missed one.

The Quiz on the 21st will be on algebra. I hope that during the week away you will have all had extra time to brush up your basic algebra skills. If you have problems please email me, or come to office hours, 2-4 Tuesday afternoon.

Note on working together

Working together on assignments is fine, and good if students can help each other to understand the material better than working on their own.

However, when people work together, the work often looks similar, and the marker has expressed concern that people have been copying from each other.

If you are working together, please can you make a statement on your work that you have been working with whoever, and state that each each student in a small group contributed equally, and eveyrone had an equal understanding of the questions, by the time you had explained to each other. If you could make this statement and sign it this will save me worrying about cheating. Thank you!


Sylabus

We will follow the book pretty closely, though sometimes going into slightly less detail, and concentrating on the main ideas (as listed below). We will cover integration only very briefly.

List of things in the sylabus:

Week1:
Functions Reiview of some algebra. What is a function, graphs of functions. Finding the equation of a line through two points. Idea of slope as rate of change.
Week2:
Limits, tangents Tangent as limit of secants. Idea of limit. Slope of tangent is the "instantaneous rate of change". Definition: derivative =slope of tangent (at a point). Finding a sequence of slopes that get closer and closer to the derivative. Continuity.
Week 3 and Week 4:
Derivatives Formulars for finding derivatives more quickly: power rule, sum rule, difference rule, product rule, quotient rule, chain rule. higher order derrivatives
Week 4 and Week 5:
Applications of derivatives Finding the equation for a tangent to a curve. Examples involving motion, eg velocity, accelleration. Related rates.
Week 6:
Extreme Values increasing and decreasing functions, maximum and minimum values; first derivative test, and examples of max/min problems.
Week 7:
Curve Sketching Sketching polynomial functions; asymtopes, concave and convex functions, second derivative test; putting this together to sketch a graph of a function.
Week8:
Trigonometric functions Explaination of what trigonometric functions are, with examples and applications, and their graphs. Some trigonometric identities. Some trigonometric equations.
Week 9:
Derivatives of trigonometric functions Derivatieves of Sine and Cosine.
Week 10:
Exponential functions Definition and explaination of exponential and logarithmic functions, and their derivatives
Week 11:
Antiderivatives Simple examples of differential equations, involving motion and exponential growth and decay.
Week 12:
Area and integration Finding the area under a graph, how this is a limit; integral notation; fundamental theorem of calculus.

Note, there may be some slight changes in order in the topics given for weeks 3, 4, 5, since I'd like to give some examples before doing all the rules, so you get an idea of what the point of all the rules is, rather than all theory, then all examples.


Course Notes

You can find a brief outline of the contents of each lecture from the links below. The numbers in brackets refer to the chapter of the course book. Note Most of the pages below are still under construction. Also these pages will only contain the main points of class, and information about the assignments; for more details, see text book, and (the day after the lecture), overheads in library.


General form of each lecture

Each lecture will be 3 hours long. This will be broken up in the following way:

Old stuff Review of last weeks stuff (15 minutes)
Quiz (15 minutes)
break (5 minutes)
New stuff preview (5 minutes)
Main part of lecture (30 minutes)
break (20 minutes)
Recap We'll go over what the new stuff was about (5 or 10 minutes)
Preview A quick look at what we'll do next time (5 or 10 minutes)
Tutorial/examples A chance to see examples done, and work on some yourself (rest of class)

Note the above is a guide line; sometimes there will be more material after the break, depending on how much has to be covered in the class.

Click here for more details on the contents of the above table.


Links

If you like surfing the web for calculus, here are some places to try.

(Thanks to Jennifer for the suggestions for the links!)


Please send corrections to spelling mistakes, and any other comments, to me.



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