Math 210: Calculus I (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 note card for the exam; see the study guide for full information.

(10/27) If you want to play around with the Desmos graph for the quadratic with its tangent lines, you can find it here.

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

(10/18) Here is the full answer key for midterm 1, including the two problems from the makeup.

(10/16) Here is an answer key to the 109 worksheet.

(10/5) You have a chance to make up lost points on the last two questions of the midterm. For each problem, if you want to earn points you lost on the midterm: do both parts of the problem and submit it to me by Friday, 10/13. If you give full correct solutions to both parts then I will update your exam grade to give you full points for the problem. Remember, the point of these problems is for you to understand the process from which the rules for derivatives come from. I will not give you points if you don’t show all steps of the process. See here for a clean pdf with just those two problems.

(10/5) Here is the answer key for midterm 1, excluding the last two problems.

(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.

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

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

(9/18) Here is a sheet of the rules for derivatives. (Note: These rules are spread across sections 3.3, 3.5, 3.6, 3.7, and 3.9 of the textbook.)

(9/11) The tutor for calc 1, Theo Lack, will be hodling review sessions on Sunday 6–7.

(8/28) Here are the introduction slides from day 1.
Homework
For each assignment I will pick among the bolded or starred 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]):
5.5 (p592) 298, 299, 301, 304, 305, 313, 316, 317
5.6 (p605) 320, 324, 326, 329, 337, 344, 345

Week 12 (due Monday 12/4):
5.4 (p575) 216, 224, 231
5.5 (p592) 254, 255, 262, 274, 282, 292, 296
*** A common form where you use substitution is when $u = kx$ for some constant $k$. In this problem you will work out the general rule for what to do in this situation.

If $u = kx$ determine $\mathrm{d}u$.

What is $\displaystyle \int e^{2x} \,\mathrm{d}x$?

What is $\displaystyle \int e^{kx} \,\mathrm{d}x$? ($k$ is a fixed constant)

What is $\displaystyle \int \sin(kx) \,\mathrm{d}x$?

What is the general rule to calculate $\displaystyle \int f(kx) \,\mathrm{d}x$, if $f$ is some function?


Week 11: No homework due to exam.

Week 10 (due Monday 11/13):
5.2 (p544) 71, 73, 78, 88, 90, 92
5.3 (p562) 144, 146, 150, 155, 170, 172, 174, 186
*** Let $k$ be an arbitrary positive integer. Figure out formulas in terms of $k$ which give the values of the definite integrals $\displaystyle \int_0^1 x^k \, \mathrm{d} x$ and $\displaystyle \int_{1}^1 x^k \, \mathrm{d} x$.

Week 9 (due Monday 11/6):
4.10 (p497) 466, 468, 470, 478, 481, 484
*** Consider the sum, for different values of $N$, given as $\displaystyle \sum_{i=1}^N \frac1{2^i}$. Compute the values of this sum for $N = 2, 3, 4, 5$. Work out a general formula for the sum for arbitrary $N$.
5.1 (p523) 14, 20, 24, 36

Week 8 (due Monday 10/30):
4.3 (p376) 90, 93, 95, 140
*** Find the numbers $x$ and $y$, subject to the constraint that the two numbers are both nonnegative and sum to $15$, which maximize the quantity $x^2y$. [Hint: If you can describe that quantity in terms of just $x$ then you want to find the maximum on the interval $[0,15]$.]
4.5 (p403) 194, 196, 206, 219, 220, 226
4.7 (p452) 324

Week 7 (due Monday 10/23):
4.1 (p350) 2, 4, 9, 10
*** do (1) of the 10/16 worksheet.
4.8 (p470) 358, 359, 360, 362, 388
*** Check that if $a < b$ are positive numbers then a runtime of $O(n^a)$ is asymptotically faster than a runtime of $O(n^b)$.
*** Check that if $a$ is any positive number then a runtime of $O(\log n)$ is asymptotically faster than a runtime of $O(n^a)$.
4.4 (p388) 148, 149.

Week 6 (due Monday 10/16):
*** Do (A) of the 10/9 worksheet.
*** OR: Do (B) of the 10/9 worksheet.
3.8 (p317) 302, 307, 312, 328
3.9 (p331) 346, 348, 351, 357

Week 5: No homework due to midterm Friday.

Week 4 (due Monday 9/25):
*** Use the limit definition of the derivative to show that the derivative of $\sqrt x$ is $\frac{1}{2\sqrt x}$.
*** Use the quotient rule and the rules for the derivatives of $\sin x$ and $\cos x$ to determine the derivatives of $\sec x$ and $\cot x$.
*** Use the chain rule and the product rule to derive the quotient rule.
3.3 (p263) 106, 110, 114, 115
3.5 (p285) 192, 195
3.6 (p297) 218, 220, 234
3.7 (p306) 280, 283
3.9 (p331) 331, 338

Week 3 (due Monday 9/18):
2.4 (p191) 133, 141, 145, 163, 164, 165
3.1 (p228) 13, 14, 16, 44
3.2 (p243) 54, 62, 66, 67, 78, 96, 97

Week 2 (due Monday 9/11):
2.3 (p176) 87, 91, 93, 99, 102, 106, 108
*** Use the limit rules in Theorem 2.5 (p161) to compute the limit $\lim_{x \to 3} (2x  1)^2$. Give a step by step argument, identifying the rule used at each step.
*** Use the squeeze theorem to compute the limit $\lim_{x \to 0} x^2 \cos(1/x)$. Give your answer as a paragraph along with your calculations, explaining why your calculations demonstrate what the limit is.
4.6 (p436) 261, 266, 279, 287
2.4 (p191) 158(i–iii only), 161

Week 1 (due Monday 9/4):
1.1 (p32) 37, 44;
1.2 (p59) 87, 98;
1.3 (p75) 155, 170;
1.4 (p92) 191, 216;
1.5 (p114) 243, 288;
2.2 (p155) 42, 50–54, 76, 77. [Note: chapter 1 is a review of material you should have covered in a previous class.]
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): Limits, continuity, and introduction to the derivative

Week 1: Introduction, the concept of the limit [Ch 1, 2.2]

Week 2: Limit laws, continuity [2.3, 4.6, 2.4]

Week 3: The IVT, the definition of the derivative [2.5, 3.1, 3.2]

Week 4: Rules for differentiating [3.3, 3.5, 3.6, 3.7, 3.9]

Week 5: Overspill, review, exam


Unit 2 (10/9–11/17): Applications of differentation and introduction to integration

Week 6: Rates of change, implicit differentiation, logarithmic differentation [3.4, 3.8, 3.9]

Week 7: Related rates, the mean value theorem, and L’Hôpital’s rule [4.1, 4.4, 4.8]

Week 8: Extreme values and optimization [4.3, 4.5, 4.7]

Week 9: Antiderivatives and Riemann sums [4.10, 5.1]

Week 10: Definite integrals and the fundamental theorem of calculus [5.2, 5.3]

Week 11: Overspill, review, exam


Unit 3 (11/27–12/13): Rules for integration

Week 12: Rules for integration, substitution [5.4, 5.5]

Week 13: Integration and logarithms, integrals involving inverse trig functions [5.6, 5.7]

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