MAT 125: Calculus 2

Fall 2018

Basic Information

Instructor: Jed Yang, CC221, 651-638-6405,
Office hours: Tuesday and Friday 13:30–14:30; or by appointment (instructions)
Lectures: Mod C (MWF 11:10–12:20) in CC426B
Course website: https://www.mathcs.bethel.edu/yang/mat125.18f/

Course Information

Official course description: A continuation of the equipping of students with tools for effective problem solving. Study of integration, sequences and series, and introduction to differential equations and approximation techniques. Each topic is approached from several viewpoints (graphical, numerical, algebraic) to involve students with different learning styles.
Prerequisites: MAT 124M: Calculus 1
Textbook: Deborah Hughes-Hallett, Andrew M. Gleason, et al., Calculus, 6th edition, 2012, ISBN: 9780470888537.
Materials: A calculator (scientific or graphing) with trig, log, and exponential capabilities. Student versions of Mathematica will be given to you.

Topics

Calculus 2 is a course designed to delve deeper into understanding and applying the ideas of differentiation and integration introduced in Calculus 1. Our text stresses the "Rule of Four": many mathematics problems can be approached from a numerical, graphical, algebraic, and verbal perspective. It may take time to adjust to this approach, but as we learn to consider problems from each of the four viewpoints, we will better understand the concepts and will be able to take part in more meaningful problem solving. Main topics we will cover:

Integration: techniques and applications
Sequences and series
Multivariable Calculus (a small introductory unit)
Differential equations

This course emphasizes thinking and problem solving over "rote" computational skills However, some algebraic computation and mnipulation is still important and will be tested (see Gateway Exam).

Objectives

I will guide you in learning to:

Engage in the process of doing and learning mathematics.
Think and understand mathematics as opposed to practice memorized procedures.
Make connections between different mathematical representations: in data (numerical), symbolic (algebraic), visual (graphical), and descriptive (written and verbal) forms.
Collaborate with peers both inside and outside of class.
Use technology in mathematical investigations through solving problems with authentic, real-world (sometimes "messy") contexts.
See mathematical principles at work in the natural world and in everyday life.
Understand and apply important ideas and results in Calculus.
Employ symbolic manipulation skills in the context of Calculus.

Grading

Your grade will be determined by a weighted arithmetic mean of various components with weights listed in the table on the right.

component	weight
Attendance and participation	5%
Homework and quizzes	30%
Midterm exams	35%
Projects	10%
Cumulative final exam	20%

The total score will be converted to a letter grade whose lower bounds are: 93% A, 90% A-, 87% B+, 83% B, 80% B-, 76% C+, 70% C, 66% C-, 63% D+, 58% D, 0% F.

Note that there is no preset curve of how many of each letter grade will be given. If you all do A-level work, you will each get an A. As such, you are encouraged to help each other in the pursuit of perfection.

In many courses I intentionally make one exam harder than others, which gives me information (in a mathematical sense) in separating an A performance from an A- performance. Typically, I will let you know and adjust that exam scores upward. What this means is that you should NOT care about how hard an exam is. If you do A-level work, you will get an A, regardless of the raw numerical score prior to adjustment.

Besides possibly adjusting scores upward for difficult exams, I also reserve the right to lower the grade cutoffs. Both of these help you. I will not hurt you by adjusting your exam scores downward or increasing the grade cutoffs.

Requirements

Whatever you do, work at it with all your heart, as working for the Lord, not for human masters, since you know that you will receive an inheritance from the Lord as a reward. It is the Lord Christ you are serving.
- Colossians 3:23–24 NIV

I will be trying to make these verses true for me as I work with you throughout this course, and I hope that you will, too.

Attendance and participation. I expect you to attend class. You may not notice me taking attendance during class meetings, but I will notice if you are not in class. Occasional absences will not impact your grade because what I look for is not mere attendance, but engagement and participation.

Indeed, coming to class is not just about showing up; it is also about being fully engaged in the learning experience. If you have a question, others in the class may also be wondering the same thing. So, please speak up and ask questions anytime you need to. Not only will you be helping yourself, but also you will be helping your peers. Attending office hours is another great opportunity to ask questions.

Be mindful of others. Refrain from using mobile phones or laptops for activities unrelated to the learning process. If you prefer to use laptops to take notes, please kindly sit in the back, as the screen may distract others. There is research that suggests taking notes by hand is better for long-term retention (P. A. Mueller and D. M. Oppenheimer, The pen is mightier than the keyboard, Psychological Science 25 (2014), 1159–1168).

Silence and put away mobile phones and do not use laptops for anything other than class-related activities.

It is my sincere hope that every one of you get all the points for attendance and participation.

Reading. Read the book! You should prepare for class by looking over the sections we will cover. Your aim is not to understand every detail, but to get a sense of where we are headed. Even a few minutes of pre-reading can help with class time. Be forewarned that a college math class is different than a high school math class. Because of limited class time you will need to learn some material on your own. As such, after class, read the sections carefully again to fill in the gaps. Keep up with the reading: reading large sections right before an exam is less effective!

Homework. Homework will be assigned most days. The goal of the homework is to give you an opportunity to continuously engage directly with the material. Some of the homework questions are meant to be challenging and to stretch you; simply put, I believe that the homework is where you will do the vast majority of your learning in this class. Grapple with the questions; talk to classmates about solution strategies if you are feeling stuck; do the homework.

Please staple your homework before coming to class and write your name, PO number, and homework number in the top right corner.

Homework is due at the beginning of the next class after it was assigned, unless otherwise stated. In general, late work is not accepted. If there are special circumstances, talk to the instructor. To alleviate your anxiety from accidentally forgetting to bring your homework to class, illness, emergencies, or other situations beyond your control, the lowest three (3) assignments will be dropped.

Because communicating results to others is an important skill, showing your work is as important as getting an answer. In many instances, credit will only be given if your work accompanies your answer. Some of the points will be given for completing the assignment; most will be awarded for showing work and correctness. You are encouraged to collaborate, but what you turn in must be your own work. See "Learning integrity" and the collaboration policy below.

Projects. We will have a project on numerical methods of integration. This project will utilize Mathematica to help us solve more significant real world problems. It will require some writing as well. It is possible we may have a second, smaller project later on in the term, as time allows. Late projects will receive a 25% deduction in points if turned in within 24 hours, 50% if turned in within 48 hours, and so on.

Exams. There are three in-class midterm exams (see calendar below for a tentative schedule), weighted equally. Subsequent exams will mainly focus on the material covered since the previous exam, but can include previous material too. There will be a final exam during the official final exam period covering the entire course.

There are no make-up exams except in circumstances recognized by the instructor as beyond the control of the student. To receive this consideration, the instructor must be notified of the problem before the exam unless this is impossible, in which case as soon as possible.

Gateway Exam. With the widespread use of calculators and programs like Mathematica, an interesting phenomenon has been observed; students have shown increased proficiency using technology, but at the same time, have lost the ability to do routine problems by hand. At Bethel, we want students to understand the concepts, be able to work elementary problems by hand (manipulative skills), and also use technology to solve extended problems that we would not have considered doing by hand previously. The Math Department has decided that it is necessary for all Calculus 2 students to demonstrate a minimal level of proficiency in working standard integral problems by hand via our Gateway Exam.

The Gateway Exam covers methods of integration and will be given after these topics have been studied in Chapter 7. See the calendar below for the first in-class exam date. Students not passing the exam will have up to four (4) opportunities to retake similar forms of the exam by the completion date given on the calendar. Passing requires that you correctly solve 5 out of the 6 problems. No partial credit is given, the problem must be completely correct. Failure to pass the exam by the completion date, will result in a reduction of your final grade by one full letter (e.g. a B+ would change to a C+). A handout containing topics and expected skills for the Gateway Exam will be given prior to the exam.

Time outside of class. I expect a typical student to spend about two to three hours outside of class for each hour in class. Some students need to spend a bit more than that (which is okay). If you are spending more than 12 hours per week on this course outside of class time, please come talk to me so we can find ways to help you learn the material without spending so much time.

Illness. You should make every effort to attend class when you are healthy. If you become ill, for your well-being and the well-being of the rest of the class, you should not come to class. (Nor should you show up in my office with your germs!) Yes, this sounds like common sense, but it is tempting to try and power through as normal so as not to fall behind. If you become ill, or know that you will need to miss class for some reason, please contact me as soon as you are able, and we will work together to plan how you will keep up and/or make up any missed work.

Policies

Learning integrity.

Search me, O God, and know my heart;
Try me, and know my anxieties;
And see if there is any wicked way in me,
And lead me in the way everlasting.
- Psalm 139:23–24 NKJV

Collaborative work is an integral part of many successful ventures. As such, I expect that you should collaborate with your classmates a lot during your time in this course. However, it is important to understand that there is a big difference between thinking about and solving a problem as part of a group (which is good, both educationally and morally) and copying an answer or letting someone else copy your answer (which is bad, educationally and morally, and has punitive consequences).

In short, I trust you to maintain the utmost level of academic integrity in this course. Please do not break this trust; if you do, there will be repercussions. The formal policy below lays this out explicitly, and supplements Bethel's academic honesty policy.

Collaboration policy.

You may collaborate on the homework assignments to the extent of formulating ideas as a group, but you may not collaborate in the actual writing of solutions (unless explicitly allowed in the instructions).
In particular, you may not work from notes taken during collaborative sessions.
You may not consult any materials from any previous offerings of this course or from any other similar course offered elsewhere unless explicitly permitted.
You are required to completely understand any solution that you submit and, in case of any doubt, you must be prepared to orally explain your solution to me. If you have submitted a solution that you cannot verbally explain to me, then you have violated this policy.

Accommodation policy. Disability-related accommodations are determined by the Office of Disability Resources and Services (DRS). Students are responsible to contact the Office of Disability Resources and Services. Once DRS determines that accommodations are to be made, they will notify the student and the instructor via e-mail. Students choosing to use the disability-related accommodations must contact the instructor no later than five business days before accommodations are needed. The instructor will provide accommodations, but the student is required to initiate the process for the accommodations.

Concerns and appeals. If you have any concerns regarding the course, your grades, or the instructor, see the instructor first. If needed, see Bethel's academic appeals policy.

Getting Help

If you need help there are multitude of resources you can use:

Yourself. If you're stuck on a problem or struggling with a concept from class, take a break and think about something else (e.g., your Hebrew assignment, the economics of Star Trek) for a few hours and then try a fresh start.
Your classmates. You are each other's best resource: talking through the course material with someone else who is also trying to master it is a great way for you both to learn. (And don't discount the learning that you will do while trying to explain to a classmate an idea covered during class that you think you understand; I can't count the number of times that I've discovered that I didn't really understand something until I tried to teach it to someone.) The homework assignments are meant to challenge you, and figuring some of them out together is a great approach.
Math Lab. The Math Department offers support for students enrolled in math classes by providing a Math Lab four days per week in HC 113 and 114. If you are having any difficulty with your homework in this class, please seek help from the tutors in Math Lab. The Math Lab is not only a great place to get help from tutors, but also is the perfect place to meet other students from class, do homework, and check your work. Plan Math Lab hours into your weekly schedule and develop this habit early on in the course.
If you attend Math Lab at least once within the first five days it is open (8/30, 9/4-6,9), you will receive 5 extra credit homework points. Be sure to sign-in and you must stay for at least 15 minutes. This is a one-time extra credit offer, not for each time you're there. The point is to get you there early in the semester so you discover it is helpful.
The instructor. Come to my office hours or email to make an appointment. To make an appointment, please email me several times you are available and try to give me at least 24 hours of lead time. Each afternoon, I will look at your availabilities and try to schedule as many people as I can fit for the next day. I will consistently reserve Thursdays for research, and I do not schedule office hours or make appointments for that day. I have this scheduled "research day" so that I can work on my research projects in an uninterrupted block of time. Without reserving a large block, I won't have time for any research. Tuesdays tend to be good days for appointments.

Calendar

Daily/weekly schedule to be updated throughout the term; topics and exam dates are tentative and subject to change.

Before class, please read the textbook section(s) to be covered. After class, start doing the homework assigned that day as soon as possible. Unless otherwise stated, homework will be due at the beginning of next class.

Date Agenda Homework
Week 1

1. 08/27 M Introduction; Chapter 5 review hw01: Getting started
2. 08/29 W Mathematica (Mma) crash course hw02: Review
3. 08/31 F 6.1, 6.2 construct antiderivatives hw03: 6.1 # 8, 9, 12, 13, 15 (plot x against t), 19, 28.
6.2 # 5, 28, 32, 36, 58*, 64, 67 (show the plot), 82.
Additional problem*: find $\int\left(t \sqrt t + \frac{1}{\sqrt t}\right)dt$.
* For 6.2#58 and additional problem: check using Mma, attach printout.
Week 2

4. 09/05 W 6.3 differential equations hw04: 6.3 # 1, 7, 9, 11, 14, 16, 20, 26*, 29.
26: Do parts (b) and (c) on Mma. For part (c), somehow label the particular solution with drawing tools or by hand. Print and attach.
Extra credit: estimate height of CLC lounge. Hand this in as a separate page, thanks.
5. 09/07 F 6.4 fundamental theorem
- chain rule
hw05: 6.4 # 1*, 3*, 9, 13, 16, 23, 39, 41.
Additional problem: find $\frac{d}{dx}\int_x^1 \ln(t)\,dt$.
* For starred problems, use Mma (download palette from Moodle) with $n=100$.
Read project description, brainstorm data set, bring laptop next class.
Week 3: Chapter 7 integration

6. 09/10 M 7.5 numerical integration
7. 09/12 W 7.5
8. 09/14 F 7.1 substitution hw08: 7.1 # 16, 19, 20, 22, 27, 28, 35, 37, 39, 53, 54, 56, 141.
Additional problem: find $\int \sin^3x\,dx$ using the identity $\cos^2x+\sin^2x=1$ and $\sin^3x=\sin^2x\cdot\sin x$.
Week 4

9. 09/17 M 7.2 by parts hw09: 7.1 # 58, 68, 78, 115, 116, 123.
7.2 # 5, 6 (use #5), 9, 20.
Additional problems:
(A) $\int(\sin^2\theta\cos^5\theta)\,d\theta$
(B) $\int_0^{1/\sqrt2}\frac{x}{\sqrt{1-x^4}}dx$.
10. 09/19 W 7.4 partial fractions hw10: 7.2 # 13, 21, 22, 29, 35, 40, 41, 54.
7.4 # 39, 47.
11. 09/21 F 7.3 tables hw11: Handout.
Week 5

12. 09/24 M 7.6 improper integrals hw12: None; study for the exam!
13. 09/26 W 7.7 comparison hw13: 7.6 # 12, 16–19, 21 (may use table), 36, 37, 43.
Additional problem: $\int_1^2\frac{dx}{x \ln x}$.
Due Monday.
14. 09/28 F Exam 1 (topics and tips)
Week 6: Chapter 8 applications of integration

15. 10/01 M 8.1 volumes by slicing hw15: 7.7 # 12*, 14, 15, 21, 22*, 24, 26b.
* For starred problems, first prove the integral converges and find an upper bound, then use a Do loop on Mma as we did in class to integrate with NIntegrate.
16. 10/03 W 8.2 solids of revolution hw16: 8.1 # 17*, 18*, 32, 35, 37.
8.2 # 43, 44.
* Show one slice first.
17. 10/05 F Gateway (topics and tips) hw17: 8.2 # 6, 9, 14, 18, 19, 38*, 39*, 46, 47, 67*.
For underlined problems, set up, but do not evaluate, the integrals.
* 38, 39: set up, but do not evaluate, the Riemann sums.
* 67: Use Mma; add ,Reals to NSolve like this: NSolve[expression,variable,Reals].
Week 7

18. 10/08 M 8.4, 8.5 physics hw18: 8.4 # 5, 6, 16*, 22.
Use NIntegrate on Mma to evaluate all integrals in 8.4.
* 16c: use trial and error.
8.5 # four additional problems listed at the end of handout.
19. 10/10 W 8.7, 8.8 probability and statistics hw19: 8.7 # 1, 21, 24.
8.8 # 2, 7, 10.
Week 8: Chapter 9 sequences and series

20. 10/15 M 9.1 sequences hw20: 9.1 # 3, 4, 11, 12, 15, 17*, 19*, 20*, 24*, 25, 28, 42, 43, 54.
* For starred problems, also plot with Mma as we did in class.
21. 10/17 W 9.2 geometric series hw21: 9.2 # 9, 10, 15*, 22, 33, 35, 46.
* 15: Also find the sum of the series for all possible $x$ values.
22. 10/19 F 9.3 series
Last day for Gateway
hw22: 9.3 # 5, 6, 9 (also draw a supporting picture), 10, 12, 15, 19, 21 (may use table), 24, 33, 37.
Week 9: Chapter 10 using series

23. 10/22 M 9.4 convergence hw23: 9.4 # 3–9 (odd only), 12–15, 20, 22–25, 35, 42, 44.
24. 10/24 W 10.1 Taylor polynomials hw24: 10.1 # 1, 6*, 15, 19, 21a, 29, 37*.
Computer all Taylor polynomials by hand, except 37a.
* 6: Also use Mma to plot the function and polynomials together in the same graph, with $x$ from 0 to 2.
* 37a: You may use Mma (in which case, print and attach).
25. 10/26 F 9.5, 10.2 power series hw25: 9.5 # 1–3, 19–21.
10.2 # 6*, 25*.
* 6: Do this by hand, using technique from 10.1, not the binomial series on p.549.
* 25: Use Mma.
Week 10

26. 10/29 M 10.2, 10.3 Taylor series hw26: 10.3 # 1, 5, 9, 24, 26, 33, 38.
Due Monday.
27. 11/02 F Exam 2 (topics and tips)
Week 11: Chapter 11 differential equations

28. 11/05 M 10.4 Taylor approximations hw28: 10.3 # 21, 35.
10.4 # 5, 7, 15, 18, 19, 21, 22.
29. 11/07 W 10.5 Fourier series hw29: 10.5 # 5, 8*, 11*, 12*, 15*.
You may, of course, check your answers with Mma, but please do all integrals by hand.
Hints for doing less work:
8: Use symmetry to deduce that half of the coefficients are 0. Use table formula to calculate the other half.
11, 15: Try to NOT actually integrate anything. Think!
12, 15: Use the result of 10 as we got in class.
30. 11/09 F 11.1 differential equations hw30: Handout.
Week 12

31. 11/12 M 11.2 slope fields hw31: Handout.
Bring laptop next class.
32. 11/14 W 11.3 Euler's method hw32: Handout.
33. 11/16 F 11.4 separation of variables
11.5 growth and decay
hw33: Handout.
Week 13: giving thanks

34. 11/19 M 11.6–11.8 modeling hw34: 11.5 # 2, 9*, 21, 24, 27ab.
* 9: plot slope field with Mma; print and attach.
11.6 # 10 (assume no leaves at first), 19, 25a.
11.7 # 8abc*, 25ab.
* 8a: sketch all solution curves on a single plot by hand with quality of a 30-second sketch.
Bring laptop next class.
Week 14: multivariable calculus

35. 11/26 M modeling with Mathematica hw35: Moodle.
36. 11/28 W Multivariable functions hw36: Handout.
37. 11/30 F Exam 3 (topics and tips)
Week 15

38. 12/03 M Multivariable differentiation hw38: Handout.
39. 12/05 W Multivariable optimization hw39: Handout.
40. 12/07 F Multivariable integration hw40: None.
Final Exam: 12/10 Monday 11:30–13:30 (topics and tips)

Date	Agenda	Homework
Week 1
1. 08/27 M	Introduction; Chapter 5 review	hw01: Getting started
2. 08/29 W	Mathematica (Mma) crash course	hw02: Review
3. 08/31 F	6.1, 6.2 construct antiderivatives	hw03: 6.1 # 8, 9, 12, 13, 15 (plot x against t), 19, 28. 6.2 # 5, 28, 32, 36, 58, 64, 67 (show the plot), 82. Additional problem: find $\int\left(t \sqrt t + \frac{1}{\sqrt t}\right)dt$. * For 6.2#58 and additional problem: check using Mma, attach printout.
Week 2
4. 09/05 W	6.3 differential equations	hw04: 6.3 # 1, 7, 9, 11, 14, 16, 20, 26, 29. 26: Do parts (b) and (c) on Mma. For part (c), somehow label the particular solution with drawing tools or by hand. Print and attach. Extra credit*: estimate height of CLC lounge. Hand this in as a separate page, thanks.
5. 09/07 F	6.4 fundamental theorem - chain rule	hw05: 6.4 # 1, 3, 9, 13, 16, 23, 39, 41. Additional problem: find $\frac{d}{dx}\int_x^1 \ln(t)\,dt$. * For starred problems, use Mma (download palette from Moodle) with $n=100$. Read project description, brainstorm data set, bring laptop next class.
Week 3: Chapter 7 integration
6. 09/10 M	7.5 numerical integration
7. 09/12 W	7.5
8. 09/14 F	7.1 substitution	hw08: 7.1 # 16, 19, 20, 22, 27, 28, 35, 37, 39, 53, 54, 56, 141. Additional problem: find $\int \sin^3x\,dx$ using the identity $\cos^2x+\sin^2x=1$ and $\sin^3x=\sin^2x\cdot\sin x$.
Week 4
9. 09/17 M	7.2 by parts	hw09: 7.1 # 58, 68, 78, 115, 116, 123. 7.2 # 5, 6 (use #5), 9, 20. Additional problems: (A) $\int(\sin^2\theta\cos^5\theta)\,d\theta$ (B) $\int_0^{1/\sqrt2}\frac{x}{\sqrt{1-x^4}}dx$.
10. 09/19 W	7.4 partial fractions	hw10: 7.2 # 13, 21, 22, 29, 35, 40, 41, 54. 7.4 # 39, 47.
11. 09/21 F	7.3 tables	hw11: Handout.
Week 5
12. 09/24 M	7.6 improper integrals	hw12: None; study for the exam!
13. 09/26 W	7.7 comparison	hw13: 7.6 # 12, 16–19, 21 (may use table), 36, 37, 43. Additional problem: $\int_1^2\frac{dx}{x \ln x}$. Due Monday.
14. 09/28 F	Exam 1 (topics and tips)
Week 6: Chapter 8 applications of integration
15. 10/01 M	8.1 volumes by slicing	hw15: 7.7 # 12, 14, 15, 21, 22, 24, 26b. * For starred problems, first prove the integral converges and find an upper bound, then use a `Do` loop on Mma as we did in class to integrate with `NIntegrate`.
16. 10/03 W	8.2 solids of revolution	hw16: 8.1 # 17, 18, 32, 35, 37. 8.2 # 43, 44. * Show one slice first.
17. 10/05 F	Gateway (topics and tips)	hw17: 8.2 # 6, 9, 14, 18, 19, 38, 39, 46, 47, 67. For underlined problems, set up, but do not evaluate, the integrals. 38, 39: set up, but do not evaluate, the Riemann sums. * 67: Use Mma; add `,Reals` to `NSolve` like this: `NSolve[expression,variable,Reals]`.
Week 7
18. 10/08 M	8.4, 8.5 physics	hw18: 8.4 # 5, 6, 16, 22. Use `NIntegrate` on Mma to evaluate all integrals in 8.4. 16c: use trial and error. 8.5 # four additional problems listed at the end of handout.
19. 10/10 W	8.7, 8.8 probability and statistics	hw19: 8.7 # 1, 21, 24. 8.8 # 2, 7, 10.
Week 8: Chapter 9 sequences and series
20. 10/15 M	9.1 sequences	hw20: 9.1 # 3, 4, 11, 12, 15, 17, 19, 20, 24, 25, 28, 42, 43, 54. * For starred problems, also plot with Mma as we did in class.
21. 10/17 W	9.2 geometric series	hw21: 9.2 # 9, 10, 15, 22, 33, 35, 46. 15: Also find the sum of the series for all possible $x$ values.
22. 10/19 F	9.3 series Last day for Gateway	hw22: 9.3 # 5, 6, 9 (also draw a supporting picture), 10, 12, 15, 19, 21 (may use table), 24, 33, 37.
Week 9: Chapter 10 using series
23. 10/22 M	9.4 convergence	hw23: 9.4 # 3–9 (odd only), 12–15, 20, 22–25, 35, 42, 44.
24. 10/24 W	10.1 Taylor polynomials	hw24: 10.1 # 1, 6, 15, 19, 21a, 29, 37. Computer all Taylor polynomials by hand, except 37a. * 6: Also use Mma to plot the function and polynomials together in the same graph, with $x$ from 0 to 2. * 37a: You may use Mma (in which case, print and attach).
25. 10/26 F	9.5, 10.2 power series	hw25: 9.5 # 1–3, 19–21. 10.2 # 6, 25. * 6: Do this by hand, using technique from 10.1, not the binomial series on p.549. * 25: Use Mma.
Week 10
26. 10/29 M	10.2, 10.3 Taylor series	hw26: 10.3 # 1, 5, 9, 24, 26, 33, 38. Due Monday.
27. 11/02 F	Exam 2 (topics and tips)
Week 11: Chapter 11 differential equations
28. 11/05 M	10.4 Taylor approximations	hw28: 10.3 # 21, 35. 10.4 # 5, 7, 15, 18, 19, 21, 22.
29. 11/07 W	10.5 Fourier series	hw29: 10.5 # 5, 8, 11, 12, 15. You may, of course, check your answers with Mma, but please do all integrals by hand. Hints for doing less work: 8: Use symmetry to deduce that half of the coefficients are 0. Use table formula to calculate the other half. 11, 15: Try to NOT actually integrate anything. Think! 12, 15: Use the result of 10 as we got in class.
30. 11/09 F	11.1 differential equations	hw30: Handout.
Week 12
31. 11/12 M	11.2 slope fields	hw31: Handout. Bring laptop next class.
32. 11/14 W	11.3 Euler's method	hw32: Handout.
33. 11/16 F	11.4 separation of variables 11.5 growth and decay	hw33: Handout.
Week 13: giving thanks
34. 11/19 M	11.6–11.8 modeling	hw34: 11.5 # 2, 9, 21, 24, 27ab. 9: plot slope field with Mma; print and attach. 11.6 # 10 (assume no leaves at first), 19, 25a. 11.7 # 8abc, 25ab. 8a: sketch all solution curves on a single plot by hand with quality of a 30-second sketch. Bring laptop next class.
Week 14: multivariable calculus
35. 11/26 M	modeling with Mathematica	hw35: Moodle.
36. 11/28 W	Multivariable functions	hw36: Handout.
37. 11/30 F	Exam 3 (topics and tips)
Week 15
38. 12/03 M	Multivariable differentiation	hw38: Handout.
39. 12/05 W	Multivariable optimization	hw39: Handout.
40. 12/07 F	Multivariable integration	hw40: None.
Final Exam: 12/10 Monday 11:30–13:30 (topics and tips)