Math 211: Calculus II (Fall 2023)
 See here for the syllabus.
Announcements

(12/8) Next week I have modified office hours to allow time for oral finals. I will be in my office Wednesday 12/13 9:00–10:00 and 3:30–4:30 and Friday 12/15 9:00–10:00.

(11/29) Here is the answer key for midterm 2.

(11/28) Here are the questions for the oral final. You will schedule a time to meet with me to present your solutions to two of the problems. Full instructions, including the grading rubric for the final, are in the pdf. The link to the signup sheet will be sent via email.

(11/10) I’m holding extra office hours the week of the midterm, so you have plenty of opportunity for last minute questions before the exam and for your metacognition meetings:
Monday 8:30–9:30, 2:30–3:30
Tuesday 2:00–4:00
Wednesday 8:30–10:00, 2:30–4:00
Friday 9:00–10:00

(11/7) Remember that the second midterm is Friday, November 17th. You will also need to turn in your unit 2 metacognition on the 17th after the exam, and you will need to do a checkin with me during office hours that week.

(11/7) Here is a study guide for the second midterm. You are allowed a onepage note sheet for the exam; see the study guide for full information.

(10/23) Remember there is no class Wednesday 10/25.

(10/18) If you want to know more about what Galois did to show the unsolvability of the quintic and aren’t happy with a brief “this would be an entire algebra class”, the wikipedia page for Galois has a short statement of what he showed. And clicking some of the links will give you an idea of how much theory needs to be built up to get at Galois’s proof.

(10/5) Here is the answer key for midterm 1.

(9/27) To turn in your unit 1 metacognition diary on Friday, 9/29: after the exam you should have one final entry, reflecting on the unit as a whole. After you finish that, either email me your diary or drop off a physical copy at my office. (If I’m not there, leave it in the mailbox.)

(9/25) For the midterm week I am holding extra office hours. In addition to the times on the syllabus, I’ll be in my office M 2:30–3:30, T 9:00–11:00, W 8:30–9:00 and 3:30–4:00.

(9/22) For the midterm, you will get a formula sheet with the formulas for arc length and surface area. For the other formulas you need: if you can remember the picture for breaking the problem up into infinitely small pieces, that picture gives you the formula.

(9/19) Remember that the first midterm is Friday, September 29th.

(9/19) Here is a study guide for the first midterm.

(9/11) The tutor for calc 2, Cathy Zhang, will be holding review sessions on Fridays 6–7pm.
Homework
For each assignment I will pick 2 to 4 of the bolded problems to grade and give you feedback on. That will comprise 80% of your grade for the assignment, with the remaining 20% being based on completion.

Week 13 (due Monday 12/11 [drop off at my office]):
7.2 (p640) 64, 66, 70, 108, 115
7.3 (p660) 155, 157, 162, 183, 185
7.4 (p669) 188, 204, 205, 217, *219

Week 12 (due Monday 12/4):
4.1 (p362) 8, 18, 20, 33
4.3 (p391) 123, 128, 133
*** Do problem (6) from the 1129 worksheet, reproduced here: You have an outdoor saltwater pool, as is normal in the Berkshires. The pool has a volume of 15,000 gallons. You want it to have the salinity of seawater, 35 parts per thousand of salt per water, which comes out to .3 lb of salt for each gallon of water. You miscalculated the size of your pool and put in 5500 lb of salt, which is too much. To fix this, you drain the pool at the rate of 5 gallons per minute while simultaneously filling it with fresh water at the rate of 5 gallons per minute. Meanwhile, you constantly stir the water to keep it the salt distribution uniform. Write a differential equation which describes the change in the quantity s of salt in the pool (in pounds) at time t (in minutes). Solve this differential equation to determine how long you need to drain the pool and refill it with fresh water to reach the optimal salt level of 4500 lb.
7.1 (p623) 49, 50, 54

Week 11: No homework due to exam.

Week 10 (due Monday 11/13):
6.1 (p541) 1, 2, 3, 8
6.2 (p568) 63, 64, 88, 110
6.3 (p578) 116, 152, 155
6.4 (p596) 202, 204, 230, 231, 232

Week 9 (due Monday 11/6):
5.3 (p482) 144, 153, 161
5.4 (p493) 198, 211, 218, 246
5.5 (p505) 250, 264, 298, 299
5.6 (p522) 323, 332, 341

Week 8 (due Monday 10/30):
5.1 (p447) 2, 3, 29, 32, 38
5.2 (p466) 68, 70, 80, 87, 88, 90
*** Write the number $0.142857142857\ldots$ as a geometric series, and use this to write it as a fraction.
*** Determine whether the series $\sum_{n=1}^\infty \frac{1}{\sqrt n}$ converges or diverges by comparing it to an appropriate improper integral.

Week 7 (due Monday 10/23):
3.7 (p343) 348, 353, 355, 358, 401, 404.
3.4 (p308) 184, 190, 198, 199.
*** Without actually computing it, explain the steps you would take to evaluate the integral $\int_{1}^1 \frac{x^5 + 5x}{(x^2  4)^2(x^2 + 4)} \,\mathrm{d}x$. As part of your answer, determine the denominators that appear in the partial fraction decomposition (but don’t compute their numerators!). And explain for each term in the partial fraction decomposition what method you would use to integrate that part.

Week 6 (due Monday 10/16):
3.1 (p270) 6, 7, 16, 41
*** Can you use integration by parts to evaluate $\int x^{1000}e^x \,\mathrm{d}x$? If so, explain what the process would be and why you know your process would eventually give an answer. If not, explain why the process won’t ever give an answer. (Please don’t actually try to compute this integral!)
*** Same question but for $\int e^x \ln x \,\mathrm{d}x$. (Again, please don’t try to actually compute it!)
3.2 (p283) 73, 74, 96, 121, 124, 125

Week 5: No homework due to midterm Friday.

Week 4 (due Monday 9/25):
2.6 (p217) 261, 262, 268
*** The uniform probability distribution on an interval $[a,b]$ is the one given by the distribution function $\rho(x) = \frac{1}{ba}$, with the domain $a \le x \le b$. Check that this really is a probability distribution function and determine its mean. Write a sentence or two giving an intuitive explanation for why its mean should be what you calculated.
2.7 (p230) 296, 298, 299, 322, 332, 333
2.8 (p141) 348, 357, 367, 374–376

Week 3 (due Monday 9/18):
2.4 (p180) 166, 168, 170, 176, 180, 185, 196, 205, 216
2.5 (p199) 223, 226, 239

Week 2 (due Monday 9/11):
2.2 (p150) 62, 68, 75, 77, 83, 88, 100
2.3 (p166) 130, 132, 140, 143

Week 1 (due Monday 9/4):
1.4 (p73) 209, 210;
1.5 (p90) 255, 276;
1.6 (p103) 320, 328;
1.7 (p111) 392;
2.1 (p131) 5, 6, 9, 35. [Note: chapter 1 is a review of material you should have covered in calc 1.]
Inclass Worksheets
Schedule
This course is organized into three units. Units 1 and 2 each end in a midterm, while unit 3 ends in an oral final discussion. Homework is assigned weekly (except on exam weeks), and is due Monday the following week.
The schedule below is tentative; we might have small adjustments in the dates. For each week I’ve included which sections from the textbook we will be covering.

Unit 1 (8/28–9/29): Applications of integration

Week 1: Intro, review, area between curves [1.4, 1.5, 1.6, 1.7, 2.1]

Week 2: Volume [2.2, 2.3]

Week 3: Arc length, surface area, applications to physics [2.4, 2.5]

Week 4: Moments, center of mass, integration and logarithms [2.6, 2.7, 2.8]

Week 5: Overspill, review, exam


Unit 2 (10/9–11/17): Advanced integration, series

Week 6: Integration by parts, trig integrals [3.1, 3.2]

Week 7: Improper integrals, partial fractions [3.4, 3.7]

Week 8: Intro to sequences and series [5.1, 5.2, 5.3]

Week 9: Tests for convergence and divergence [5.4, 5.5, 5.6]

Week 10: Power series [6.1, 6.2, 6.3]

Week 11: Overspill, review, exam


Unit 3 (11/27–12/13): A preview of future classes

Week 12: Intro to ODEs, parametric equations [4.1, 4.3, 7.1]

Week 13: Parametric calculus, polar coordinates [7.2, 7.3, 7.4]

Week 14: Overspill, review

Important dates:

Friday, Sept 29: Midterm 1 and first diary due

Friday, Nov 17: Midterm 2 and second diary due

Oral Final Discussion: Scheduled individually with me, TBA