preparation

Fri Aug 31

Mon Sep 3

• Sections 1.1 to 1.3 of Strang.

Wed Sep 5

• None

Fri Sep 7

• Sections 1.4 and 1.5 of Strang

Mon Sep 10

• No preparation needed for class but note that the first graded assignment is due today at 3pm.

Wed Sep 12

• None

Fri Sep 14

• Strang 2.1 - 2.3.

Fri Sep 21

• Strang 2.4

Mon Sep 24

• Strang 2.5

Wed Sep 26

• Strang 2.6 and2.7

Fri Sep 28

• none

Mon Oct 1

• Have a go at the homework and identify any issues you are having with it.

Wed Oct 3

• None (Assignment 2 due at 3pm today).

Fri Oct 5

• Strang 3.2, 3.3 and 3.4.

Mon Oct 8th

Wed Oct 10th

• Thoroughly read Strang 3.4. Here's my recipe for doing so.

• Read through the whole section quickly, to get a sense for the topics that are going to be covered.
  • Note that there are 6 main points under "Mechanics of Graphs". Write them down in big letters on a separate sheet of paper, possibly changing things around so that they're in your own words. Stick this sheet of paper where you can see it when you are working.
  • Work carefully through Examples 1 and 2, making sure you understand each step.
  • Answer questions 5 and 7 (chosen for their similarity to Examples 1 and 2).
  • Work carefully through Example 3.
  • Answer questions 11 and 17 (chosen for their similaritly to Example 3).
  • Read through the "read through" questions making sure you can fill them in.
  • The rest of the section looks more at graphing calculators. We'll return to that topic (with Mathematica rather than graphing calculators) later in the semester. Make sure you have a sense of the main issues though.
  • Try a few more questions. Take them from the region 3-17 (odd) if you think you need more practice along the lines of the examples. Take them from 19-31 to extend the ideas further.
• You might also supplement this with video from the MIT site by Strang, or from elsewhere (feel free to share any good relevant ones you find).

Fri Oct 12th

• Strang 3.5. The recipe:
  • First read through: understand the conic section picture (Fig 3.15) and keep a note of the general similarities and differnces in each of the main sections (parabola, ellipse, hyperbola).
  • Work through several examples to make sure you understand them. It's a little harder to be specific this time around because this material draws on a lot of things you've probably seen before the class but may have forgotten or be rusty on (completing the square, equations of circles, trig to perform rotations,...). You'll have to do some brushing up on these.
  • Questions 3-13 (odd) are ideal for testing if you've got the basic ideas down; the rest are more demanding but if you get time try a few odd numbered ones.
  • Now go back and fill in any of the reading that you skimmed and didn't have to refer to to complete the questions you did---it should fill in the remaining gaps.

Wed Oct 17th

Fri Oct 19th

• Strang 3.8 up to, but not including, the remark on p. 151.
  • Read through, paying close attention to the careful statements of the results and making sure you can follow the examples.
  • Questions 1-9 (odd) are good practice for MVT and 13-21 (odd) for l'Hopital.
  • Read back through the chapter with (possibly) the deeper understanding that you've gained from the exercises.
  • There are a lot more interesting questions at the end of this section that get under the skin of these ideas. Try some.

Week starting Mon Oct 22nd

• Strang 4.1
  • Make sure you understand function composition, especially Example 4.1. Skip Example 4.2.
  • Read the rest of the chapter, focusing on the statement of the Chain Rule and carefully following the examples. Skip the proof at the first reading.
  • Questions 1-25 (odd) are all good practice. Do as many as it takes to become automatic (you can find more practice elsewhere too if this is insufficient; let me know if you need pointers). This is possibly the most difficult of the differentiation rules that you need to be able to just do when needed (we'll see plenty of stuff that's more complicated, but you won't be expected to do it automatically).
  • Go back and read the proof of the rule and perhaps try some of the later questions that you like the look of.

• Strang 4.2. This one comes in two halves, implicit differentiation and related rates problems.
  • Read the implicit differentiation theory and carefully follow the examples.
  • Questions 1-9 (odd) give some practice. As in 4.2 this is a topic on which you might need more practice than Strang provides at the easier questions to master the idea.
  • Read the related rates, again carefully following the examples. Examples 5 to 8 give a good sense of the type of problem for which this method is useful.
  • Questions 21-29 (odd) are good practice.

Monday Oct 29th

• Strang 4.3 and 4.4. We discussed the main ideas in class on Friday. Go through and check out the details and get some practice in.
  • Box 4C expresses what we did in a different way. Make sure you understand what that is saying and how it connects with what we did in class.
  • Don't worry too much about the exponentials and logarithms section in 4.3: we'll be looking in a lot more detail at these functions in a few weeks.
  • Follow the arguments for deducing the derivatives of the inverse trig functions.
  • Select appropriate practice problems and do them.

Wednesday Oct 31st to Monday Nov 5th

• Strang 5.3 (as far as the bottom of p. 192).
  • Play with Sigma notation until you understand it and can manipulate them effectively. Questions 1-7 odd might help.
  • Follow the method of finding the area under the parabola \(y = x^2\), noting the similarities and differences with us finding the area under \(y=x\) in class.
• Strang 5.4.
  • Make sure you understand the list on p. 196 and where they all came from (they're our standard differentiation rules rephrased as "antiderivative" rules).
  • Linearity should not be surprising or difficult. Buried in this section is an important tip though: you can usually check an integral easily by differentiating your answer and ensuring it matches the function you wanted to integrate.
  • Substitution is important and can be difficult or, at least, not obvious what to substitute.
  • Doing all of questions 1-19 (odd) is probably worth your time.
• Assignment due Monday 5th Nov.

Wednesday Nov 7th to Monday Nov 12th

• Strang 5.5:
  • The first third should be familiar from in-class conversations. Make sure you understand it all, especially the difference and relationship between indefinite and definite integrals.
  • The second third gives a more sophisticated approach to Riemann sums than the one we used in class. Can you see how our approach fits in?
  • The remarks of the final third are optional but interesting.
  • 11-17 (odd) are good questions to do.
• Strang 5.6:
  • Make sure you understand the reasons for Properties 1-6 in terms of areas under graphs.
  • For average values and the stats examples, focus mostly on Property 7 and understanding the average value calculation method.
  • 1-5 (odd) are good for the average value; 9-15 (odd) for Proprties 1-6.
  • Question 29 is lovely.
• Strang 5.7:
  • FTC1 and FTC2: We've been using them both, now you get to see why they're true.
  • Read through the applications and try some of the associated exercises.

Friday Nov 16th

By Wedneasday Nov 21st

• Strang 6.1: Mostly an introduction to exponentials and logarithms, and so probably a review for most of you. Work on it as much as you need to. Don't worry too much about the log paper piece. The derivatives section at the end is probably new; we'll see more detail in Section 6.2, but Eq10 at the bottom of p.233 is important.
• Strang 6.2: The number \(e\) and the function \(e^x\). Now we can differentiate it, it we can add it to our bag of differentiation/integration tricks. Good practice: questions 1-17 (odd) and 27-35 (odd).
• Strang 6.4: As 6.2 but with \( \ln x\). Good practice: questions 1-23 (odd).