MAT 125: Calculus 2
Spring 2019
Basic Information
- Instructor: Jed Yang, CC221, 651-638-6405,
- Office hours: by appointment (instructions)
- Lectures:
- Section 1: Mod C (MWF 11:10–12:20) in RC229
- Section 2: Mod F (MWF 14:50–16:00) in RC229
- Course website: https://www.mathcs.bethel.edu/yang/mat125.19s/
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: Chapter 6 antidifferentiation | ||
1. 02/04 M | Introduction; Chapter 5 review | hw02ab: Getting started |
2. 02/06 W | Mathematica (Mma) crash course | hw03ab: Review |
3. 02/08 F | 6.1, 6.2 construct antiderivatives | hw04a: 6.1 # 8, 9, 12, 13, 15 (plot x against t), 19, 28.
hw04b: 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 58 and additional problem: check using Mma, attach printout. Both assignments are due next class; please staple separately. |
Week 2 | ||
4. 02/11 M | 6.3 differential equations | hw05a: 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. hw05b: Extra credit: estimate height of AC lounge. |
5. 02/13 W | 6.4 fundamental theorem | hw06a: 6.4 # 1*, 3*, 9, 13, 16, 23, 39, 41, 42.
* For starred problems, use Mma (download palette from Moodle) with $n=100$. hw06b: Read project description, brainstorm data set, bring laptop next class. |
6. 02/15 F | 7.5 numerical integration | |
Week 3: Chapter 7 integration techniques | ||
7. 02/18 M | 7.5 | |
8. 02/20 W | 7.1 substitution | hw09: 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 $\sin^3x=\sin^2x\cdot\sin x$. There is only one part in this assignment; remember that proj1f is also due next class. |
9. 02/22 F | 7.2 by parts | hw10a: 7.1 # 58, 68, 78, 115, 116, 123.
hw10b: 7.2 # 5, 6 (use #5), 9, 20. Additional problems:
|
Week 4 | ||
10. 02/25 M | 7.4 partial fractions | hw11a: 7.2 # 13, 21, 22, 29, 35, 40, 41, 54.
hw11b: 7.4 # 39, 47. |
11. 02/27 W | 7.3 tables | hw12ab: Handout. |
12. 03/01 F | 7.6 improper integrals, type 1 | None; study for the exam! |
Week 5 | ||
13. 03/04 M | 7.6 improper integrals, type 2 | None; study for the exam, seriously! |
14. 03/06 W | Exam 1 (topics and tips) | hw15: 7.6 # 12, 16–19, 21 (may use table), 36, 37, 43.
Additional problem: $\int_1^2\frac{dx}{x \ln x}$. |
15. 03/08 F | 7.7 comparison | hw16: 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. |
Week 6: Chapter 8 applications of integration | ||
16. 03/11 M | 8.1 volumes by slicing | hw17: 8.1 # 17*, 18*, 32, 35, 37.
8.2 # 43, 44. * Show one slice first. |
17. 03/13 W | 8.2 solids of revolution Gateway (topics and tips) | hw18: 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]. |
18. 03/15 F | 8.4, 8.5 physics | hw19a: 8.4 # 5, 6, 16*, 22.
Use NIntegrate on Mma to evaluate all integrals in 8.4. * 16c: use trial and error. hw19b: 8.5 # four additional problems listed at the end of handout. |
Week 7: spring break | ||
Week 8: Chapter 9 sequences and series | ||
19. 03/25 M | 8.7, 8.8 probability and statistics | hw20a: 8.7 # 1, 21, 24.
hw20b: 8.8 # 2, 7, 10. |
20. 03/27 W | 9.1 sequences | hw21: 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. 03/29 F | 9.2 geometric series | hw22: 9.2 # 9, 10, 15*, 22, 33, 35, 46.
* 15: Also find the sum of the series for all possible $x$ values. |
Week 9: Chapter 10 using series | ||
22. 04/01 M | 9.3 series | hw23: 9.3 # 5, 6, 9 (also draw a supporting picture), 10, 12, 15, 19, 21 (may use table), 24, 33, 37. |
23. 04/03 W | 9.4 convergence
Last day for Gateway | hw24: 9.4 # 3–9 (odd only), 12–15, 20, 22–25, 35, 42, 44. |
24. 04/05 F | 10.1 Taylor polynomials | hw25: 10.1 # 1, 6*, 15, 19, 21a, 29, 37*.
Compute 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). |
Week 10 | ||
25. 04/08 M | 9.5, 10.2 power series | None; study for the exam! |
26. 04/10 W | Exam 2 (topics and tips) | hw27: 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. |
27. 04/12 F | 10.2, 10.3 Taylor series | hw28: 10.3 # 1, 5, 9, 21, 24, 26, 33, 35, 38. |
Week 11 | ||
28. 04/15 M | 10.4 Taylor approximations | hw29: 10.4 # 5, 7, 15, 18, 19, 21, 22. |
29. 04/17 W | 10.5 Fourier series | hw30: 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. |
Week 12: Chapter 11 differential equations | ||
30. 04/24 W | 11.1 differential equations | hw31: Handout |
31. 04/26 F | 11.2 slope fields | hw32: Handout Bring laptop next class. Also bring hw33 handout to class, with at least 1a filled out. |
Week 13 | ||
32. 04/29 M | 11.3 Euler's method | hw33: Handout |
33. 05/01 W | 11.4 separation of variables 11.5 growth and decay | hw34: Handout |
34. 05/03 F | 11.6–11.8 modeling | hw35: 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. 05/06 M | modeling with Mathematica | hw36: Moodle |
36. 05/08 W | Multivariable functions | hw37: Handout |
37. 05/10 F | Multivariable differentiation | None; study for the exam! |
Week 15 | ||
38. 05/13 M | Exam 3 (topics and tips) | hw39: Handout |
39. 05/15 W | Multivariable optimization | hw40: Handout |
40. 05/17 F | Multivariable integration | None; study for the exam! |
Final Exam: 05/21 Tuesday 11:30–13:30 (Section 1) and 14:45–16:45 (Section 2) |
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: 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
- Differential equations
- Multivariable Calculus (a small introductory unit)
This course emphasizes thinking and problem solving over "rote" computational skills. However, some algebraic computation and manipulation 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, projects, and quizzes | 39% |
Midterm exams | 36% |
Cumulative final exam | 20% |
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.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.- Colossians 3:23–24 NIV
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.
Typically, there will be two (2) assignments due each class. Please staple each assignment separately before coming to class. Write your name, PO number, and homework number in the top right corner. Failure to do so may result in loss of credit.
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 five (5) 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. You must email the instructor within 2 hours of the original deadline to receive this consideration.
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 software 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+).
More information
regarding 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 to 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.
Learning integrity.
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.
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.
If you attend Math Lab at least once within the first five days it is open (Feb 7, 10–13),
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.
Policies
Search me, O God, and know my heart;
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).
Try me, and know my anxieties;
And see if there is any wicked way in me,
And lead me in the way everlasting.
Getting Help
If you need help there are multitude of resources you can use: