Course:MATH110/Archive/2010-2011/003/Lectures

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Next Reading: Lecture 38 - Friday January 7

For this lecture, you are asked to prepare two things:

  • First, to review logarithms. Group 14 wrote about that in their basic skills project page, check it out.
  • Second, work on finding the size in bits of the content of Wikipedia if we use the following statistics:
    • There are 3.4 million articles.
    • Each article has an average of 242 words.
    • Each word has an average of 6 characters (5 letters and a space or punctuation).

Lecture 38 - Friday January 7

For this lecture, you are asked to prepare two things:

  • First, to review logarithms. Group 14 wrote about that in their basic skills project page, check it out.
  • Second, work on finding the size in bits of the content of Wikipedia if we use the following statistics:
    • There are 3.4 million articles.
    • Each article has an average of 242 words.
    • Each word has an average of 6 characters (5 letters and a space or punctuation).

Lecture 27 - Friday November 12

In this lecture, we will study the notion of elasticity which is used in economics to better understand the influence of a change of the output of a system for a given change of input. This should be of interest to everybody as the main focus will not be economics itself, but how to apply the mathematics that we have learned so far in a precise context; and how to use the derivative to get information about a function.

This lecture will heavily rely on group activity, hence, I recommend you encourage all your other group members to attend class.

Class setup: Groups 9 and 10 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 26 - Wednesday November 10

Read the note on the product rule which we will discuss in class again and start practicing as soon as possible. Exercices are recommended at the end of the note.

Class setup: Groups 11 and 12 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 24 - Friday November 5

In this lecture, we will start discussing formulas that allow us to compute derivatives. Starting with fundamental properties of derivatives, we'll aim for the power rule, which allows us to compute the derivative of any polynomial very easily. We'll see how to use this and will also discuss a reasonable proof to justify this formula.

If time permits, we will discuss problem 2c and 6c from the midterm.

Class setup: Groups 13 and 14 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 23 - Wednesday November 3

This lecture will focus on two topics. The first one is more conceptual and talks to the idea of the derivative as a function. Getting started with the webwork assignment titled Week9 is an excellent preparation for this. The second topic is more technical and will explain how to compute sign tables of functions. This technique has many applications, for example, it would provide a lot of help when it comes to do a problem such as problem 8 from the Week8 webwork assignment that 57% of you failed to solve.

Class setup: Groups 15 and 16 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 22 - Monday November 1

I want to take some time today to reflect on the midterm and discuss the end-game for this term. That's why I'm asking all of you to be present and punctual for this discussion to be constructive and valuable to all.

Lecture 21 - Friday October 29

In this class, we'll discuss how to compute derivatives using the tools of limits and will apply this to study a few examples. At the end of this class you should be able to:

  • Explain how to use limits to compute derivatives,
  • Compute the derivative of some easy functions using limits.

Class setup: Groups 17 and 18 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 20 - Wednesday October 27

We'll continue our discussion of asymptotes with the study of vertical asymptotes. Then we'll move on and discuss some problem solving strategies and see some examples in class. Following this discussion, I'll update my notes on asymptotes. At the end of this class you should be able to:

  • Define vertical asymptotes,
  • Explain how to figure out whether a function has any vertical asymptotes or not.

Class setup: Groups 1 and 2 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 19 - Monday October 25

Today we'll discuss a first approach to derivatives.

Lecture 18 - Friday October 22

Read my notes on asymptotes, we'll continue our discussion in class.

Then do the 5 problems that I've assigned on a the WeBWorK, the set is called Lecture18 of course. This tests your understanding of limits at infinity and what a horizontal asymptote is.

Class setup: Groups 3 and 4 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 17 - Wednesday October 20

Two goals for today:

  • Finish our discussion about continuity,
  • Discuss the concept of asymptotes.

Class setup: Groups 5 and 6 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 16 - Monday October 18

Let's get back to limits today and work more precisely on how to compute them. I've modified my notes on continuity to add some content that was discussed in class on Friday, check it out! The goal is to create the material for a new note on limits that is currently empty. We'll put in there whatever you feel is necessary. For this, first go read my first note on what are limits? and then try to solve some problems, the goal is to talk about the problems you're having a hard time to solve.

So, from the textbook, section 2.3, work on problems 23-34, 37-48, 56-63. If you find yourself struggling a bit, that's good! That's how it should feel like, just solving all the problems in one shot means they're too easy and you're learning nothing. Doing mathematics means spending a lot of time trying to solve problems, so if this is what is happening to you, you're on the right track, it most certainly does not mean that you're dumb. (If you think of it, when at the gym, you must sweat a little, otherwise it means you're not doing much, again: no pain, no gain).

And if you haven't done so in a while, it's worth checking some of the earlier reading assignments, they might contain some useful information, who knows?

Lecture 15 - Friday October 15

Today we'll do the following things:

  • Discuss the concept of continuity of functions,
  • Have a Q&A session on how to compute limits.

In order to be able to participate fully to this lecture, you're required to read the notes on continuity and do the problems mentioned at the end of that page. Reading mathematics is a skill to learn, I recommend you read the first half of this article by Shai Simonson and Fernando Gouvea. An hour or two spend at this will greatly increase the learning you'll be able to achieve from your reading and save you a good deal of frustration too.

The Q&A session will be based on your questions only, so make sure you have some ready.

Have a look at the page I created for working on the basic skills project. Any questions or comments? Just go to that page's discussion tab and start the conversation.

Class setup: Groups 7 and 8 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 14 - Wednesday October 13

Class setup: Groups 9 and 10 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 13 - Friday October 8

Now that we have discussed what are limits, we'll spend this lecture discussing how to compute them. Read section 2.3 carefully. Forget about example 5 (page 68) for now. What can you say about the following limits?

We'll discuss those in class. I suggest starting working through problems 1 to 48 of this section. Make sure you do at least problems 11, 19, 25, 33, 35 and 45. Warm-up questions will be on this material.

Class setup: Groups 11 and 12 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 12 - Wednesday October 6

We'll talk about trigonometric functions today and will spend 10min discussing your questions. Read section 1.4 until page 39. On that page, read the first half on transforming graphs but no about inverse trigonometric functions we won't need that for now.

Then read again sections 2.1 and 2.2, think how this relates to what we discussed on Monday. Work on exercises 1-15 and 19 from section 2.2 (pages 61-62). Warm-up questions will cover similar material.

Class setup: Groups 13 and 14 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 11 - Monday October 4

This is the beginning of week 5 and the homework is due today. So, for Monday, read section 2.1 and 2.2 of the Calculus textbook. Focus on the ideas and examples. If for instance you don't really know or remember trigonometric functions, then either read about them in chapter 1 or just skip, the focus here is on what is a limit, not the technology used to showcase it. I'll ask questions regarding to some of the first exercises of section 1.2 in the warm-up.

Class setup: Groups 15 and 16 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 10 - Friday October 1

Read section 1.2 of the Calculus: Early Transcendentals text. We'll take time again in class to discuss the project due on Monday, make good use of that time!

Class setup: Groups 17 and 18 are in charge of placing the tables in three rows of 6 before class and putting them back in order at the end of class.

Lecture 9 - Wednesday September 29

Read section 1.1 of the Calculus: Early Transcendentals text.

Lecture 8 - Monday September 27

We'll discuss the homework for a few minutes in class, if you got in this course late, have a look at the homework page and give it a try. For those who wrote an essay in the wiki, I've added a few comments in the discussion tab of your page, check it out. I've also compiled a list of some selected essays that I think were of good quality, you can find this liste here.

Now, the action for this week is on proofs. What are they? Well, I want you to research over the web and see what you can find. To get you started on the topic I selected three pages to read on three important questions you might ask yourselves:

We will spend the week discussing proofs: how to write them, how to find them, how to share them. This doesn't mean proofs vanish the week after, it simply means we get to spend some time just discussing about them, we'll keep seeing proofs throughout the rest of the course.

Skills Test - Friday September 24

Passing the Skills Test (passing means, get a passing grade) will grant you 5% of your final grade (as long as you pass the test, we don't really care about your grade on the test). If you do not pass this test, there will be ways throughout the term to get these 5% back through some extra work.

Lecture 7 - Wednesday September 22

You will be taking the skills test on Friday, it mostly covers chapters 1 to 4 from the Just-In-Time textbook, so make sure you read those chapters carefully and try as many problems as possible. If you have questions, feel free to use the Math Forum or add specific questions here, I will select some of them to be discussed on Wednesday.

Lecture 5 - Friday September 17

The reading for this Friday is sections 3.3 and sections 4.4, 4.5 and 4.6 of Just-In-Time Algebra & Trigonometry for Calculus. Two warm-up questions will be asked on this material at the beginning of class.

The reading goals of section 3.3 are to be able to:

  • remember the four basic tools suggested there when solving equations,
  • solve the equations described in this section.

Note: We're not going to spend any time on complex numbers, if you're not used to them or even never heard of them, just skip happily.

Solving equations is of course a big tool in this course, we'll keep practicing this art, but won't go over the methods later on, so make sure you know how to solve them, but don't worry if it still takes you time and efforts, that's only normal at this point.

As for sections 4.4 to 4.6, your goals for the reading are to be able to:

  • describe how to shift up, down, left right any given function,
  • explain how to combine these operations to translate any given function in any given direction.

Again, play with Wolfram|Alpha (or any other tool that can graph functions) to get a good feel of the wide range of functions and how to translate them in some directions. Sketching is an important skill, but understanding the underlining concepts here is far more important.

The recommended problems for this reading assignment are:

For 3.3
Problems 1, 2, 9, 10, 19, 20, 25, 26.
For 4.4
Problems 5, 6
For 4.5
Problems 3, 7
For 4.6
Problems 5, 6, 7, 8.

Lecture 4 - Wednesday September 15

Please read sections 3.2, 4.1 and 4.3 of Just-In-Time Algebra & Trigonometry for Calculus. Two warm-up questions relating to this reading will be asked at the beginning of the lecture. If you haven't done so yet, please register your iClicker on the Vista webpage of this course.

Your goals while reading section 3.1 are to be able to:

  • recognize an equation of degree 2 (also called quadratic equations) when given one,
  • solve these equations.

Read things carefully, wether it is new material or older material for you. Try each example on your own first before reading the solution. Make yourself some cue cards with important things to remember such as facts, definitions, formulas. Then, start practicing. The more you practice, the better you get at this (math is actually like going to the gym). If you get stuck, confused, lost, just or if you think you're actually doing pretty well, just go on the Math Forum and see what you can do there (don't forget to log in with the button at the top-right corner of the page to be able to edit content).

Section 4.1 is added to the reading material for you to make sure you recall what a function is. If some of it is unclear at first, spend some time reading the section, trying some problems or ask on the forum.

For section 4.3, your goals are to be able to:

  • recall what is a power function,
  • sketch very roughly these power functions.

Here, the focus is on the following question: If is a power function, what is the link between the shape of its graph and the value of the parameter ?. I strongly recommend you experiment it yourself by playing with Wolfram|Alpha which is a fantastic tool which will tell you many many things. Get started by simply typing f(x)=x^2 or even better, simply type polynomials and go from there.

Lecture 3 - Monday September 13

Over the weekend, the recommended reading is section 3.1 and section 4.2 of Just-In-Time Algebra & Trigonometry for Calculus. There will be a warm-up test on Monday first thing in the morning about these two sections, so make sure read them carefully and tried some exercises. Please remember to bring your iClickers in class as well, we'll need that!

Your goals while reading section 3.1 are to be able to:

  • recognize an equation of degree 1 (also called linear equations) when given one,
  • solve these equations.

I recommend reading the theory, try to solve the equations given in the examples before reading their solutions and comparing the text to what you did. Make sure you understand each step and that what is explained in the text makes sense for you. If not, write it down, it will make for a great question in class or in this wiki. After that, don't forget to try yourself at a few exercises from the section, remember you have the solutions of the odd-numbered problems. For the others, maybe you want to see how the others did by asking a question in this wiki.

For the section 4.2, your reading goals are to be able to:

  • explain what is the slop of a line,
  • determine the point-slope equation of a given line,
  • sketch the graph of a line for which you have an equation in point-slop form,
  • explain what is the y-intercept of a line,
  • determine the slope-intercept equation of a given line,
  • sketch the graph of a line for which you have an equation in the slope-intercept form

Again, you're not supposed to excel at any of these goals, but you should have a solid idea of what to do. If not, again, write this down, it makes a great question for class or for the wiki. Monday's lecture will address these goals.

In this section, make sure you try the detailed examples yourself before reading their solutions. Have a look at the proof on page 55 only once you've read the rest of the section, I don't want you to be stuck on this. We will discuss some proofs, but if you're struggling with this one now, no worries. Also, skip example 4 on page 57 if you're not comfortable with the absolute value function (this is what the means). For the example 6, recall that two lines are parallel if they have the same slope. For example 7, recall that two lines are perpendicular if the product of their slopes is (so for example, a line of slope is perpendicular to a line of slope ½).

Lecture 2 - Friday September 10

The first reading assignment consists of chapter 1 of the Just-In-Time Algebra & Trigonometry for Calculus textbook. Read every section carefully, examples included and try at least three problems from each exercise set. Answers to odd-numbered exercices are given at the end of the book. This chapter covers important concepts from arithmetic, you might be quite rusty using them but don't worry, practice makes perfect!